Skip to content

minor generalization #1433

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
CohenCyril merged 2 commits into from
Dec 18, 2024
Merged

minor generalization #1433

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
4b9af26
minor generalization
affeldt-aist Dec 10, 2024
2978c54
simplifications
CohenCyril Dec 17, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
5 changes: 4 additions & 1 deletion CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,10 @@
+ lemma `integral_measure_add`

- in `probability.v`
+ lemma `integral_distribution` (existsing lemma `integral_distribution` has been renamed)
+ lemma `integral_distribution` (existing lemma `integral_distribution` has been renamed)

- in `measure.v`:
+ lemma `countable_bigcupT_measurable`

### Changed

Expand Down
1 change: 1 addition & 0 deletions classical/classical_sets.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2602,6 +2602,7 @@ Proof.
by apply: qcanon; elim/eqPchoice; elim/choicePpointed => [[T F]|T];
[left; exists (Empty.Pack F) | right; exists T].
Qed.

Lemma Ppointed : quasi_canonical Type pointedType.
Proof.
by apply: qcanon; elim/Peq; elim/eqPpointed => [[T F]|T];
Expand Down
13 changes: 10 additions & 3 deletions theories/measure.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1390,13 +1390,20 @@ Qed.

End sigma_ring_lambda_system.

Lemma bigcupT_measurable_rat d (T : sigmaRingType d) (F : rat -> set T) :
Lemma countable_bigcupT_measurable d (T : sigmaRingType d) U
(F : U -> set T) : countable [set: U] ->
(forall i, measurable (F i)) -> measurable (\bigcup_i F i).
Proof.
move=> Fm; have /ppcard_eqP[f] := card_rat.
by rewrite (reindex_bigcup f^-1%FUN setT)//=; exact: bigcupT_measurable.
elim/Ppointed: U => U in F *; first by move=> *; rewrite empty_eq0 bigcup0.
move=> /countable_bijP[B] /ppcard_eqP[f] Fm.
rewrite (reindex_bigcup f^-1%FUN setT)//=; first exact: bigcupT_measurable.
exact: (@subl_surj _ _ B).
Qed.

Lemma bigcupT_measurable_rat d (T : sigmaRingType d) (F : rat -> set T) :
(forall i, measurable (F i)) -> measurable (\bigcup_i F i).
Proof. exact/countable_bigcupT_measurable. Qed.

Section measurable_lemmas.
Context d (T : measurableType d).
Implicit Types (A B : set T) (F : (set T)^nat) (P : set nat).
Expand Down