proposition: Lemma integrable_expectation (X : {RV P >-> R}) (iX : P.-integrable [set: T] (EFin \o X)) : `| 'E_P[X] | < +oo.
proof: Proof. move: iX => /integrableP[? Xoo]; rewrite (le_lt_trans _ Xoo)// unlock. exact: le_trans (le_abse_integral _ _ _). Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) HB(structures) exp numfun lebesgue_measure lebesgue_integral reals ereal signed topology normedtype sequences esum measure exp numfun lebesgue_measure lebesgue_integral