proposition: Lemma powR_Lnorm f r : r != 0%R -> 'N_r%:E[f] `^ r = \int[mu]_x (`| f x | `^ r)%:E.
proof: Proof. move=> r0; rewrite unlock (negbTE r0) -poweRrM mulVf// poweRe1//. by apply: integral_ge0 => x _; rewrite lee_fin// powR_ge0. 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 lebesgue_integral numfun exp convex itv