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2023 07 27 Meeting
affeldt-aist edited this page Jul 27, 2023
·
1 revision
Participants: Reynald, Cyril, Pierre, Zachary, Takafumi
- naming convention for
bigcup
:- see comment https://github.com/math-comp/analysis/issues/988#issuecomment-1651515771
- see also
bigcup_set0
vs.bigcup0
-
\bigcup_(x in ~` P) F x
, we writebigcup_setC
- in general, in
bigcup_xyz
,xyz
is about thein
part -
\bigcup_(A in P) ~` F A
, we make a longer name, we may write something likebigcup_setCr
- instead of, e.g.,
bigcupP_setC
- also, try to swap the equality as in, e.g.,
setC_bigcup
- instead of, e.g.,
- in general, in
- Discussion about the pending issues about renaming
- do not rename
ball
toopen_ball
because balls are not necessarily open - we actually need a stronger notion of pseudometric space where there is a distance between any two points
- more generally, there is a bunch of renaming about closed balls
- TODO: we should have a notion of open balls
- about
scale_cball
from the PR on Vitali's lemma:- introduce a predicate
is_ball
so that we the predicate is satisfied we have have acenter
and aradius
function - or introduce a
ball
record with a coercion to a set? - anyway, we'd like to unify the various notions of balls
- we should be aiming for
scale_ball
to be a function from balls to balls
- introduce a predicate
- do not rename
-
https://github.com/math-comp/analysis/pull/973 (Vitali's lemma)
- change the lemma from
B : I -> R * {posnum R}
to two functionsI -> R
andI -> {posnum R}
?- at least try not to expose the
scale_cball
by introducing alternative statements
- at least try not to expose the
- as of now, many lemmas could be generalize to dimension n but they are still in dimention 1
- change the lemma from
- news about perf of HB branch: thanks to latest elpi (1.17.0) and master branches of coq-elpi and HB:
- total analysis: 26:31 (used to be 40 min) (2.6 GB (used to be 10 GB))
- loading elpi code (HB): 02:59 (used to be 16 min)
- running elpi code (HB): 08:55
- not all elpi code is released so MathComp-Analysis 1 can maybe wait a bit
- PR triaging:
- merge https://github.com/math-comp/analysis/pull/985 ?
- can be merged
- putting the
N <= i
cond in the hypo or not? (maybe not)
- merge https://github.com/math-comp/analysis/pull/971 ?
- Cyril: isn't 1/3 automatically a posnum?
- division by 2 gets thing automatically inferred by not division by 3 (!)
- TODO: Pierre to investigate
- work around: replace
3
with3%:R
- work around: replace
- TODO: make the 1/3 disappear before merge if possible
- NB: we can use lra for mathcomp-analysis from now
- TOD0: add the dependency to algebra tactics
- Cyril: isn't 1/3 automatically a posnum?
-
https://github.com/math-comp/analysis/pull/973
- pending question about where to put lemmas about centered intervals
- they appear in Lebesgue's differentiation theorem for continuous functions
- we might need a more general approach to represent balls (see the discussion above)
- we will hit the problem quickly when moving to higher dimensions anywau
- pending question about where to put lemmas about centered intervals
-
https://github.com/math-comp/analysis/pull/984 (Vitali's theorem)
- TODO: Zachary to review
-
https://github.com/math-comp/analysis/pull/995 (Hardy-Littlewood)
- TODO: Zachary to get rid of the the boundeness hypo in the inner regular lemma
- differentiation theorem is around the corner
- for the easiest approach using Radon-Nikodym we need absolute continuity for functions (this should be the last piece)
- Zachary spotted an appropriate proof on stack overflow
- Takafumi: we might also need bounded variation
-
https://github.com/math-comp/analysis/pull/900 (Urysohn's Lemma)
- TODO: Zachary to update following Cyril's comment
- goal: merge it in the next days (as well as Tietze)
- relies on a technical proof (see
step_ball
, Step 1, Step 2, Step 3 intopology.v
) - uniform spaces with countable basis:
- merge https://github.com/math-comp/analysis/pull/985 ?