proposition: Lemma pr_eq0 mu E : \P_[mu] E = 0 -> forall x, x \in E -> mu x = 0.
proof: Proof. move/eq0_psum=> /(_ (summable_pr _ _)) => h x xE; move/(_ x): h. by move: xE; rewrite -topredE /= => ->; rewrite mul1r. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp classical_sets mathcomp_extra) xfinmap ereal reals discrete topology realseq realsum