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minor generalization #1433

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minor generalization #1433

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5 changes: 4 additions & 1 deletion CHANGELOG_UNRELEASED.md
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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

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1 change: 1 addition & 0 deletions classical/classical_sets.v
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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];
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15 changes: 13 additions & 2 deletions theories/measure.v
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Expand Up @@ -1390,11 +1390,22 @@ Qed.

End sigma_ring_lambda_system.

Lemma countable_bigcupT_measurable d (T : sigmaRingType d) (U : choiceType)
(F : U -> set T) : countable [set: U] ->
(forall i, measurable (F i)) -> measurable (\bigcup_i F i).
Proof.
elim/choicePpointed: U => U in F *.
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.
move=> Fm; have /ppcard_eqP[f] := card_rat.
by rewrite (reindex_bigcup f^-1%FUN setT)//=; exact: bigcupT_measurable.
apply: countable_bigcupT_measurable.
by apply/countable_bijP; exists setT; exact: card_rat.
Qed.

Section measurable_lemmas.
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