[Merged by Bors] - feat: Basic conditional probability lemmas #10785
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YaelDillies
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RemyDegenne
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| lemma law_of_total_probability {Y : Ω → α} (hY : Measurable Y) (μ : Measure Ω) [IsFiniteMeasure μ] : | ||
| μ = ∑ y, μ (Y ⁻¹' {y}) • (μ[|Y ← y]) := by |
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Can you revert this equality, and give a more descriptive name to the theorem, mentioning sum and cond?
I also don't like that name because this is not the only statement that could be called "law of total probability". For example, when I think of that law, I imagine the first of the two equalities on the wikipedia page: https://en.wikipedia.org/wiki/Law_of_total_probability . There is also the continuous case...
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What about now?
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LGTM! |
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