math sum r sup left lbrace sum j r j aleph j subseteq right rbrace math define sum math r math supremum sums finitely many measure math mu math math sigma math math kappa math additive math lambda kappa math family disjoint sets math x alpha alpha lambda math following hold math bigcup alpha lambda x alpha sigma math math mu left bigcup alpha lambda x alpha right sum alpha lambda mu left x alpha right math note second condition equivalent statement ideal null sets math kappa math complete sigma finite measures measure space called finite finite real number rather nonzero finite measures
Formal science Mathematics Pure mathematics Probability theory Measure theory