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Merged
CohenCyril merged 1 commit into from
Dec 18, 2024
Merged

add lemma measurable_powRr #1434

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7 changes: 7 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Original file line number Diff line number Diff line change
Expand Up @@ -35,6 +35,9 @@
- in `probability.v`
+ lemma `integral_distribution` (existsing lemma `integral_distribution` has been renamed)

- in `lebesgue_measure.v`:
+ lemma `measurable_powRr`

### Changed

- in `lebesgue_integrale.v`
Expand Down Expand Up @@ -100,6 +103,10 @@
- in `measure.v`:
+ `dynkin_setI_bigsetI` (use `big_ind` instead)

- in `lebesgue_measurable.v`:
+ notation `measurable_fun_power_pos` (deprecated since 0.6.3)
+ notation `measurable_power_pos` (deprecated since 0.6.4)

### Infrastructure

### Misc
23 changes: 15 additions & 8 deletions theories/lebesgue_measure.v
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Expand Up @@ -1180,9 +1180,10 @@ Proof.
move=> mf.
exact: (@measurable_comp _ _ _ _ _ _ setT (fun x : R => x ^+ n) _ f).
Qed.
#[deprecated(since="mathcomp-analysis 1.4.0", note="use `measurable_funX` instead")]
Notation measurable_fun_pow := measurable_funX (only parsing).

Lemma measurable_powR (R : realType) p :
measurable_fun [set: R] (@powR R ^~ p).
Lemma measurable_powR (R : realType) p : measurable_fun [set: R] (@powR R ^~ p).
Proof.
apply: measurable_fun_if => //.
- apply: (measurable_fun_bool true).
Expand All @@ -1194,14 +1195,20 @@ apply: measurable_fun_if => //.
Qed.
#[global] Hint Extern 0 (measurable_fun _ (@powR _ ^~ _)) =>
solve [apply: measurable_powR] : core.
#[deprecated(since="mathcomp-analysis 0.6.3", note="use `measurable_powR` instead")]
Notation measurable_fun_power_pos := measurable_powR (only parsing).
#[deprecated(since="mathcomp-analysis 0.6.4", note="use `measurable_powR` instead")]
Notation measurable_power_pos := measurable_powR (only parsing).

Lemma measurable_powRr {R : realType} b : measurable_fun [set: R] (@powR R b).
Proof.
rewrite /powR; apply: measurable_fun_if => //.
- rewrite preimage_true setTI/=.
case: (b == 0); rewrite ?set_true ?set_false.
+ by apply: measurableT_comp => //; exact: measurable_fun_eqr.
+ exact: measurable_fun_set0.
- rewrite preimage_false setTI; apply: measurableT_comp => //.
exact: mulrr_measurable.
Qed.

#[deprecated(since="mathcomp-analysis 0.6.3", note="use `measurable_maxr` instead")]
Notation measurable_fun_max := measurable_maxr (only parsing).
#[deprecated(since="mathcomp-analysis 1.4.0", note="use `measurable_funX` instead")]
Notation measurable_fun_pow := measurable_funX (only parsing).

Module NGenCInfty.
Section ngencinfty.
Expand Down