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[Merged by Bors] - feat(measure_theory/interval_integral): introduce ∫ x in a..b, f x, prove FTC-1#3640
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[Merged by Bors] - feat(measure_theory/interval_integral): introduce ∫ x in a..b, f x, prove FTC-1#3640
∫ x in a..b, f x, prove FTC-1#3640Conversation
We have a general `norm_zero` lemma and these lemmas are not used before we introduce `normd_group` instances.
Also use `variables {s t : set α}`
A compact set `s` has finite (resp., zero) measure if every point of `s` has a neighborhood within `s` of finite (resp., zero) measure.
∫ x in a..b, f x, prove FTC-1 (deps: 3663, 3685, 3686)∫ x in a..b, f x, prove FTC-1
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Yury, could you rebase this on master please?
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I've recently merged |
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The goal is simply to have a reviewable diff. Right now it seems the diff tab is indeed reasonable, but I'm almost sure it wasn't when I asked for a rebase. Maybe my browser didn't update the page. |
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Now I have a version with |
sgouezel
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This looks very good, I only have minor comments. I'd rather merge this one and postpone your improvements to another PR, if you don't mind.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
…nity/mathlib into interval-integral
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bors r+ |
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… prove FTC-1 (#3640) Define `∫ x in a..b, f x ∂μ` as `∫ x in Ioc a b, f x ∂μ - ∫ x in Ioc b a, f x ∂μ`. With this definition for a probability measure `μ` we have `F_μ(b)-F_μ(a)=∫ x in a..b, f x ∂μ`, where `F_μ` is the cumulative distribution function.
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∫ x in a..b, f x, prove FTC-1∫ x in a..b, f x, prove FTC-1
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Define
∫ x in a..b, f x ∂μas∫ x in Ioc a b, f x ∂μ - ∫ x in Ioc b a, f x ∂μ. With this definition for a probability measureμwe haveF_μ(b)-F_μ(a)=∫ x in a..b, f x ∂μ, whereF_μis the cumulative distribution function.Depends on
#3618, #3642, #3643, #3645, #3647, #3652, #3653, #3663 #3685 #3686.I hope that the rest can be reviewed in one chunk. Tell me please if you prefer me to further split this PR.