proposition: Lemma Lnorm1 f : 'N_1[f] = \int[mu]_x `|f x|%:E.
proof: Proof. rewrite unlock oner_eq0 invr1// poweRe1//. by apply: eq_integral => t _; rewrite powRr1. by apply: integral_ge0 => t _; rewrite powRr1. 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