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addressing comments
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affeldt-aist committed Aug 24, 2024
1 parent d7f42ad commit b66a9ae
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4 changes: 2 additions & 2 deletions theories/lebesgue_integral.v
Original file line number Diff line number Diff line change
Expand Up @@ -3391,8 +3391,8 @@ have [r0|r0|->] := ltgtP r 0%R.
Qed.

Lemma integralZr r :
\int[mu]_(x in D) (f x * r%:E) = r%:E * \int[mu]_(x in D) f x.
Proof. by rewrite -integralZl; under eq_integral do rewrite muleC. Qed.
\int[mu]_(x in D) (f x * r%:E) = (\int[mu]_(x in D) f x) * r%:E.
Proof. by rewrite muleC -integralZl; under eq_integral do rewrite muleC. Qed.

End linearityZ.
#[deprecated(since="mathcomp-analysis 0.6.4", note="use `integralZl` instead")]
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2 changes: 1 addition & 1 deletion theories/probability.v
Original file line number Diff line number Diff line change
Expand Up @@ -159,7 +159,7 @@ Qed.

Lemma expectationM (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 -integralZr. Qed.
Proof. by rewrite unlock muleC -integralZr. Qed.

Lemma expectation_ge0 (X : {RV P >-> R}) :
(forall x, 0 <= X x)%R -> 0 <= 'E_P[X].
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