## A first course in measure and integration |

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### Contents

Section CHAPTER I MEASURES 1 Rings and rings | 1 |

The lemma on monotone classes | 4 |

Set functions measures | 7 |

30 other sections not shown

### Common terms and phrases

a.e. PROOF absolute continuity AC with respect assume Borel set bounded complement fn(x convergence in measure COROLLARY countably additive definition disjoint union dominated convergence E U F exists a measurable extended real numbers extended real valued f and g f dp f is integrable f is measurable f U g Fatou's lemma finite measure space finite signed measure fm(x fn dp formula Fubini's theorem function f g are measurable g dp gn(x hence f I(fn integrable function integrable with respect integral of f iterated integral Jf dp Let f liminf limsup locally measurable set measurable function monotone class monotone convergence theorem moreover mutually disjoint notation null set outer measure pointwise Radon-Nikodym theorem real valued functions Riesz-Fischer theorem ring sequence f sequence of measurable sequence of sets set function Similarly simple functions Suppose f T-finite uniform convergence valued functions defined