feat(probability): define conditional probability and add basic related theorems #12279
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rish987
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rish987
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Feb 25, 2022
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| local notation μ `[` s `|` t `]` := cond μ t s | ||
| local notation μ `[|` t`]` := cond μ t |
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Noticed that this conflicts with some existing notation for conditional expectation -- let me know what you think is best here, will be happy to change.
eric-wieser
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Feb 25, 2022
| /-- The conditional probability measure of any finite measure on any set of positive measure | ||
| is a probability measure. -/ | ||
| instance cond_is_probability_measure [is_finite_measure μ] {s : set α} (hcs : μ s ≠ 0) : | ||
| is_probability_measure $ μ[|s] := |
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I think it would be worthwhile to attempt to tweak the notation so that no $ is needed here.
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I agree, not sure what was going on here. Don't have much experience defining notation so suggestions are welcome. I'd also be OK with just doing without notation here for now.
ericrbg
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Please push this branch to mathlib repo and PR to the master branch from there, as described in the contributor guidelines. |
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Add the definition of conditional probability as a scaled restricted measure and prove Bayes' Theorem and other basic theorems.