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Lebesgue differentiation for continuous functions #972
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- minor gen. of integral_le_bound - move lemmas to more appropriate locations - rebase on master to use measurable_compact
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I proposed a few minor improvements in the last commit.
I would like also to propose to use ball x r
instead of ] x - r, x +r[
otherwise it looks like
we are not using an already available identifier that could make it clearer to put together
lemmas about centered, open intervals (that are also important in Vitali's lemma and theorem which also have lemmas about centered, closed intervals).
Also, what about using "r +* 2" instead of "2 * r"? There are many lemmas about the former in ssrnum.v
that could maybe trigger small optimizations in calculation steps.
I do not want to make these blocking requests because arguably these are minor issues but being homogeneous about these presentation issues could help factorizing further results.
last commit was just to fix the changelog |
These suggestions seem very sensible. I'll make an update in the next day or two. |
The last commit is only minor fixes, I'll mege as soon as the CI is as green as it can be. |
(I changed the changelog because the new |
* interval topology facts * weakening continuity * minor improvements - minor gen. of integral_le_bound - move lemmas to more appropriate locations - rebase on master to use measurable_compact * using ball instead of intervals in the statement * using natmul notation --------- Co-authored-by: Reynald Affeldt <[email protected]>
* interval topology facts * weakening continuity * minor improvements - minor gen. of integral_le_bound - move lemmas to more appropriate locations - rebase on master to use measurable_compact * using ball instead of intervals in the statement * using natmul notation --------- Co-authored-by: Reynald Affeldt <[email protected]>
More work towards fundamental theorem of calculus, this is the "easy" part of the last track in #965. Most of the proof is shuffling around absolute values signs and standard error bounds. The only interesting detail is that we really do need
f
to be integrable in a neighborhood aroundx
otherwise it's not clear what the limit actually means.I prove a couple lemmas that could maybe go in a more helpful location. If you have recommendations, I'm happy to oblige.
Motivation for this change
Things done/to do
CHANGELOG_UNRELEASED.md
[] added corresponding documentation in the headersCompatibility with MathComp 2.0
TODO: HB port
to make sure someone ports this PR tothe
hierarchy-builder
branch or I already opened an issue or PR (please cross reference).Automatic note to reviewers
Read this Checklist and put a milestone if possible.