## Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable |

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### Contents

Set Theory and Algebra | 1 |

Relations and functions | 7 |

The axiom of choice and some equivalents | 12 |

Copyright | |

22 other sections not shown

### Common terms and phrases

a-algebra a-finite absolutely continuous algebra apply arbitrary assertion Banach space Borel measurable Borel sets called cardinal number Cauchy sequence choose closed compact Hausdorff space compact set complete complex measure complex number complex-valued function consider constructed contains continuous functions converges countably additive Definition dense element equality Exercise exists extended real-valued finite measure Fourier Fubini's theorem function defined function g Hence Hilbert space Hints holds hypothesis implies inequality infinite inner product space integral Lebesgue measurable Lemma Let f Let g Let H linear subspace locally compact locally compact Hausdorff mapping measurable function measure space metric space nonvoid set normed linear space notation obtain obvious one-to-one open set open subset outer measure positive integer positive number positive real number Proof reader real-valued function Riemann-Stieltjes integrable signed measure space and let Suppose t-measurable topological space topology trivial uniformly unique write zero