proposition: Lemma sintegralE f : sintegral mu f = \sum_(x \in range f) x%:E * mu (f @^-1` [set x]).
proof: Proof. rewrite (fsbig_widen (range f) setT)//= => x [_ Nfx] /=. by rewrite preimage10// measure0 mule0. 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