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2020 09 28 Meeting
affeldt-aist edited this page Sep 28, 2020
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Participants: Marie, Cyril, Kazuhiko, Pierre-Yves, Reynald
- PR 179 (https://github.com/math-comp/analysis/pull/179)
- has been rebased, on top of PR 183 (https://github.com/math-comp/analysis/pull/183)
- displays 114 commits
- might require a
rebase --onto
- might require a
- the introduction of entourages in the hierarchy is not transparent
- use
nbhs_ballP
? look at the files of the merge PR 242 (https://github.com/math-comp/analysis/pull/242/files) for illustration?
- use
- TODO: put in the header documentation information about crucial lemmas (
nbhs_ballP
?)
- PR 183 (https://github.com/math-comp/analysis/pull/183)
- TODO: split into several PRs
- one with linear-continuous stuff only
- one with
closed_ball
(btw, add compacity to it) for further discussion - one with Landau notations (but this is for later)
- TODO: split into several PRs
- PR 262 (https://github.com/math-comp/analysis/pull/262)
- introduces
closed_ball
which is often more practical than open balls (avoid cutting epsilon's in half)
- introduces
- stalled PRs
- PR 205 (https://github.com/math-comp/analysis/pull/205), doubts that it might go as expected
- PR 204 (https://github.com/math-comp/analysis/pull/204), application envisioned
- PR 180 (https://github.com/math-comp/analysis/pull/180)
- problems with filter types can be addressed by selecting
simpl
's
- problems with filter types can be addressed by selecting
- TODO: have the CI handle hb (e.g., in https://github.com/math-comp/analysis/pull/224)
- PR 224 (https://github.com/math-comp/analysis/pull/224)
- Progress report about integral_sketch:
- started with the file
integral.v
written by the meeting participants some time ago (just a sketch, in particular no proofs,measurableType
not available, theory of extended real numbers under-developed) - since then, we have merged into master:
- a theory of sequences of real numbers (
sequences.v
) - the pseudometric structure of extended real numbers
- a small theory of sequences of extended real numbers
- the basics of
measurableType
(with the proof of the Boole inequality (measure.v
))
- a theory of sequences of real numbers (
- during this summer, we have:
- further developed the theory of sequences of extended real numbers (PR 264)
- developed a small theory of countable sums (http://fourier.math.uoc.gr/~mathweb/lnotes/papadimitrakis+graduate-measure-theory.pdf definition 1.4 page 23, proposition 2.3 page 23, proposition 2.6 page 26)
- based on a small theory of countable sets (
cardinality.v
)) -
measure.v
now features a small hierarchy using hierearchy-builder (SemiRingOfSets
,RingOfSets
,Measurable
) and + definitions of "negligibe" and outer measure -
measure_wip.v
contains two proofs of interest for measure theory (https://lefevre.perso.math.cnrs.fr/PagesPerso/enseignement/Archives/Lebesgue.pdf, theorem 5 page 3 (Caratheodory's theorem), proposition 11 (construction of an outer measure from a measure))
- started with the file
- discussion on how to use proposition 11 to build Lebesgue's measure, on the use of Caratheodory-Hahn theorem
- TODO: formalize CH theorem in two steps: first the build measure
in terms of a function (
Def Hahn_measure := fun x => ...
), and then declare a Canonical instance tagged onmu_ext
(similarly to^o
) to have a measure on the generated sigma-algebra (instead of Caratheodory) - TODO: define the generated sigma-algebra using an inductive type with 3 constructors (the first one for the starting point, the other for complement and union), prove equivalence with the current definition (by intersection)
- TODO: theorem 15 by Li (construction of the ring of sets of intervals from a semi-ring of sets)
- Progress report about integral_sketch:
- Issue 255 (https://github.com/math-comp/analysis/issues/255)
- TODO: framadate with Reynald, Pierre-Yves, and Cyril to merge
realseq.v
andsequences.v
, should take less than two hourse - TODO: plan a similar meeting for countable sums after that
- TODO: framadate with Reynald, Pierre-Yves, and Cyril to merge
- TODO: merging of eudoxus reals
- Issue 261 (https://github.com/math-comp/analysis/issues/261)
- TODO: extract ereal contents from
normedtype.v
toereal.v
- TODO: extract ereal contents from