Whenever, do(𝑡) appears after the conditioning bar, it means that everything in that expression is in the post-intervention world where the intervention do(𝑡) occurs. For example, 𝔼[𝑌 | do(𝑡), 𝑍 = 𝑧] refers to the expected outcome in the subpopulation where 𝑍 = 𝑧 after the whole subpopulation has taken treatment 𝑡 .
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- (no access) - Introduction_to_Causal_Inference-Nov19_2020-Neal.pdf, p41
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