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#measure-theory

In mathematical analysis, a **measure** on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the *n* -dimensional Euclidean space **R**^{n} . For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1.

Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (*see* Definition below). It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a *consistent* size to *each* subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called *measurable* subsets, which are required to form a σ -algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement.^{[1]} Indeed, their existence is a non-trivial consequence of the axiom of choice

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[imagelink] Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. <span>In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space R n . For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1. Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (see Definition below). It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. [1] Indeed, their existence is a non-trivial consequence of the axiom of choice. Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon, and Maurice Fréchet, among others. The ma

#measure-theory

In mathematical analysis, a **measure** on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns th

[imagelink] Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. <span>In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space R n . For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1. Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (see Definition below). It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. [1] Indeed, their existence is a non-trivial consequence of the axiom of choice. Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon, and Maurice Fréchet, among others. The ma

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

[imagelink] Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. <span>In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space R n . For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1. Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (see Definition below). It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. [1] Indeed, their existence is a non-trivial consequence of the axiom of choice. Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon, and Maurice Fréchet, among others. The ma

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last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Tags

#redes #tcp-ip

Question

TCP/IP. Características Básicas

Answer

Los servicios que TCP proporciona para la comunicación entre aplicaciones, pueden caracterizarse en los cuatro puntos siguientes:

- Cuando dos aplicaciones transfieren grandes cantidades de datos, podemos pensar en esos datos como secuencias de octetos. El módulo TCP del nodo destino entrega las secuencias de octetos que recibe a la capa superior, tal y como la capa superior del nodo origen se la entregó a TCP.

- Circuito virtual: TCP proporciona un servicio de comunicación orientado a la conexión. De esta forma TCP suministra un servicio fiable de transporte de datos de extremo a extremo. Entre otros servicios, TCP proporciona el establecimiento de la conexión, la transferencia de información y la desconexión.

- Buffers de datos. Las aplicaciones transfieren sus datos en forma de cadenas de octetos al módulo TCP. Este agrupa o divide las cadenas de octetos recibidas en función del tamaño del paquete que puede transmitir. Para hacer más eficiente la transmisión y reducir el tráfico en la red, es necesario que el módulo TCP disponga de buffers donde acumular la información. Obviamente estos buffers pueden retrasar la transmisión de determinada información. Cuando es necesario realizar la transmisión inmediata de algunos datos, puede solicitarse a TCP que transmita dicha información (push), aún cuando su tamaño sea menor que el que proporciona mayor rendimiento.

- Conexión full-duplex: |TCP/IP permite que las conexiones establecidas entre dos nodos sean concurrentes o simultáneas en ambos sentidos. Las aplicaciones ven este servicio como dos canales de transmisión (uno de entrada y otro de salida), sin interacción aparente.

- Cuando dos aplicaciones transfieren grandes cantidades de datos, podemos pensar en esos datos como secuencias de octetos. El módulo TCP del nodo destino entrega las secuencias de octetos que recibe a la capa superior, tal y como la capa superior del nodo origen se la entregó a TCP.

- Circuito virtual: TCP proporciona un servicio de comunicación orientado a la conexión. De esta forma TCP suministra un servicio fiable de transporte de datos de extremo a extremo. Entre otros servicios, TCP proporciona el establecimiento de la conexión, la transferencia de información y la desconexión.

- Buffers de datos. Las aplicaciones transfieren sus datos en forma de cadenas de octetos al módulo TCP. Este agrupa o divide las cadenas de octetos recibidas en función del tamaño del paquete que puede transmitir. Para hacer más eficiente la transmisión y reducir el tráfico en la red, es necesario que el módulo TCP disponga de buffers donde acumular la información. Obviamente estos buffers pueden retrasar la transmisión de determinada información. Cuando es necesario realizar la transmisión inmediata de algunos datos, puede solicitarse a TCP que transmita dicha información (push), aún cuando su tamaño sea menor que el que proporciona mayor rendimiento.

- Conexión full-duplex: |TCP/IP permite que las conexiones establecidas entre dos nodos sean concurrentes o simultáneas en ambos sentidos. Las aplicaciones ven este servicio como dos canales de transmisión (uno de entrada y otro de salida), sin interacción aparente.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Características Básicas. Los servicios que TCP proporciona para la comunicación entre aplicaciones, pueden caracterizarse en los cuatro puntos siguientes: - Cuando dos aplicaciones transfieren grandes cantidades de datos, podemos pensar en esos datos como secuencias de octetos. El módulo TCP del nodo destino entrega las secuencias de octetos que recibe a la capa superior, tal y como la capa superior del nodo origen se la entregó a TCP. - Circuito virtual: TCP proporciona un servicio de comunicación orientado a la conexión. De esta forma TCP suministra un servicio fiable de transporte de datos de extremo a extremo. Entre otros servicios, TCP proporciona el establecimiento de la conexión, la transferencia de información y la desconexión. - Buffers de datos. Las aplicaciones transfieren sus datos en forma de cadenas de octetos al módulo TCP. Este agrupa o divide las cadenas de octetos recibidas en función del tamaño del paquete que puede transmitir. Para hacer más eficiente la transmisión y reducir el tráfico en la red, es necesario que el módulo TCP disponga de buffers donde acumular la información. Obviamente estos buffers pueden retrasar la transmisión de determinada información. Cuando es necesario realizar la transmisión inmediata de algunos datos, puede solicitarse a TCP que transmita dicha información (push), aún cuando su tamaño sea menor que el que proporciona mayor rendimiento. - Conexión full-duplex: |TCP/IP permite que las conexiones establecidas entre dos nodos sean concurrentes o simultáneas en ambos sentidos. Las aplicaciones ven este servicio como dos canales de transmisión (uno de entrada y otro de salida), sin interacción aparente.