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Rings and oRings
The Lemma on Monotone Classes
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additive algebra assertion assume Baire measure Baire set belongs Borel function Borel set bounded called chapter choose clear clearly closed compact Go's compact set completion consider contains continuous convergence Corollary countable defined definition denoted disjoint domain equivalent Evidently EXERCISES exists extended f and g finite measure fixed fn(x follows formula function f fundamental given Haar integral hence implies integrable Baire functions integrable function Lemma linear locally compact space mean measurable function measurable set measurable with respect measure space monotone moreover notation null set o-finite o-ring particular positive Proof properties real number real-valued functions rectangle regular Borel measure relation respect restriction ring Sect sequence set function Similarly simple subsets suffice Suppose Theorem theory union unique values vanishes write zero