proposition: Lemma mulemu_ge0 d (T : measurableType d) (R : realType) (mu : {measure set T -> \bar R}) x (A : R -> set T) : ((x < 0)%R -> A x = set0) -> 0 <= x%:E * mu (A x).
proof: Proof. by move=> xA; rewrite (@mulef_ge0 _ _ (mu \o _))//= => /xA ->; rewrite measure0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) signed reals ereal topology normedtype sequences real_interval esum measure lebesgue_measure numfun