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2020 09 28 Meeting

affeldt-aist edited this page Sep 28, 2020 · 3 revisions

Participants: Marie, Cyril, Kazuhiko, Pierre-Yves, Reynald

  • PR 179 (https://github.com/math-comp/analysis/pull/179)
  • 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)
  • 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)
  • stalled PRs
  • 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))
      • during this summer, we have:
    • 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 on mu_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)
  • Issue 255 (https://github.com/math-comp/analysis/issues/255)
    • TODO: framadate with Reynald, Pierre-Yves, and Cyril to merge realseq.v and sequences.v, should take less than two hourse
    • TODO: plan a similar meeting for countable sums after that
  • TODO: merging of eudoxus reals
  • Issue 261 (https://github.com/math-comp/analysis/issues/261)
    • TODO: extract ereal contents from normedtype.v to ereal.v