proposition: Lemma fin_num_fun_sigma_finite d (T : algebraOfSetsType d) (R : realFieldType) (mu : set T -> \bar R) : mu set0 < +oo -> fin_num_fun mu -> sigma_finite setT mu.
proof: Proof. move=> muoo; exists (fun i => if i \in [set 0%N] then setT else set0). by rewrite -bigcup_mkcondr setTI bigcup_const//; exists 0%N. by move=> n; split; case: ifPn => // _; rewrite fin_num_fun_lty. Qed.
imports: mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) reals ereal signed topology normedtype sequences esum numfun HB(structures)