folland real analysis chapter 1 s ebastien picard problem 1 5 if m is the algebra generated by e then m is the union of the algebras generated by f ...
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...Folland real analysis chapter s ebastien picard problem if m is the algebra generated by e then union of algebras f as ranges over all countable subsets hint show that latter object a solution let n denote count able when contained in ie sowehaven for reverse containement we rst observe indeed where j some index set next will since smallest containing have and this complete proof c therefore consider each i hence x be nite measure space ef b say an equivalence relation on dene g denes metric classes first notice it follows clear reexive ee also easy to see symmetric fe sof only remains transitive suppose fc gc eg ec must triangle inequality given fg called locally measurable msuchthat...