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Tail expectation formula for L1 random variable#1865

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Yosuke-Ito-345 wants to merge 2 commits intomath-comp:masterfrom
Yosuke-Ito-345:expectation_cdf_ccdf
Open

Tail expectation formula for L1 random variable#1865
Yosuke-Ito-345 wants to merge 2 commits intomath-comp:masterfrom
Yosuke-Ito-345:expectation_cdf_ccdf

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@Yosuke-Ito-345
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Motivation for this change

Add the tail expectation formula expectation_cdf_ccdf for any L1 random variable.
This is a combined version of lemmas ge0_expectation_ccdf and le0_expectation_cdf.

Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md

  • added corresponding documentation in the headers

Reference: How to document

Merge policy

As a rule of thumb:

  • PRs with several commits that make sense individually and that
    all compile are preferentially merged into master.
  • PRs with disorganized commits are very likely to be squash-rebased.
Reminder to reviewers

@Yosuke-Ito-345
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@affeldt-aist @t6s
I’m not sure what caused this error. Is there anything I should do on my side?

@affeldt-aist
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Here is the error message:

File "./reals/signed.v", line 6, characters 29-37:
Error: Cannot find a physical path bound to logical path
unstable with prefix mathcomp.

and here is the problematic code:

From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool.
From mathcomp Require Import ssrnat eqtype choice order ssralg ssrnum ssrint.
#[warning="-warn-library-file-internal-analysis"]
From mathcomp Require Import unstable.
From mathcomp Require Import mathcomp_extra.

I don't understand why it fails suddenly (maybe @proux01 knows)
but do not worry: signed.v is a deprecated file, I will test on my side ASAP,
worst case scenario: we don't find a fix, then we might simply give up on Coq 8.20.

@Yosuke-Ito-345
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@affeldt-aist
Thank you for investigating this error. I really appreciate your help.

@affeldt-aist
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Mmmhhh... I can't reproduce the error locally. :-(

@affeldt-aist affeldt-aist force-pushed the expectation_cdf_ccdf branch from 6ebcb05 to 86c3edd Compare March 12, 2026 10:12
@affeldt-aist
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(Sorry, I made a push force but at least it is updated w.r.t. master.)
I tried to simplify your proof using a theory for the positive/negative part of real functions taken from PR #1391 (not merged yet).
I think it is better to do the proof this way because it contributes to a theory that is useful elsewhere.
What do you think?
(I still need one pass to complete the review.)

@Yosuke-Ito-345
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@affeldt-aist
Thank you for your suggestion. I agree with you. The positive/negative part of real-valued functions is an important notion and appears everywhere in the Lebesgue integral theory.

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2 participants