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fix
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affeldt-aist committed Dec 3, 2024
1 parent 42b197f commit e592efa
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions theories/probability.v
Original file line number Diff line number Diff line change
Expand Up @@ -167,7 +167,7 @@ move: iX => /integrableP[? Xoo]; rewrite (le_lt_trans _ Xoo)// unlock.
exact: le_trans (le_abse_integral _ _ _).
Qed.

Lemma expectationMl (X : {RV P >-> R}) (iX : P.-integrable [set: T] (EFin \o X))
Lemma expectationZl (X : {RV P >-> R}) (iX : P.-integrable [set: T] (EFin \o X))
(k : R) : 'E_P[k \o* X] = k%:E * 'E_P [X].
Proof. by rewrite unlock muleC -integralZr. Qed.

Expand Down Expand Up @@ -217,8 +217,8 @@ by apply/funext => t/=; rewrite big_map sumEFin mfun_sum.
Qed.

End expectation_lemmas.
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to `expectationMl`")]
Notation expectationM := expectationMl (only parsing).
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to `expectationZl`")]
Notation expectationM := expectationZl (only parsing).

HB.lock Definition covariance {d} {T : measurableType d} {R : realType}
(P : probability T R) (X Y : T -> R) :=
Expand Down Expand Up @@ -249,7 +249,7 @@ rewrite expectationD/=; last 2 first.
- by rewrite compreBr// integrableB// compre_scale ?integrableZl.
- by rewrite compre_scale// integrableZl// finite_measure_integrable_cst.
rewrite 2?expectationB//= ?compre_scale// ?integrableZl//.
rewrite 3?expectationMl//= ?finite_measure_integrable_cst//.
rewrite 3?expectationZl//= ?finite_measure_integrable_cst//.
by rewrite expectation_cst mule1 fineM// EFinM !fineK// muleC subeK ?fin_numM.
Qed.

Expand Down Expand Up @@ -289,7 +289,7 @@ have aXY : (a \o* X * Y = a \o* (X * Y))%R.
rewrite [LHS]covarianceE => [||//|] /=; last 2 first.
- by rewrite compre_scale ?integrableZl.
- by rewrite aXY compre_scale ?integrableZl.
rewrite covarianceE// aXY !expectationMl//.
rewrite covarianceE// aXY !expectationZl//.
by rewrite -muleA -muleBr// fin_num_adde_defr// expectation_fin_num.
Qed.

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