## Elements of real analysis |

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### Contents

SETS FUNCTIONS AND RELATIONS 1 Sets | 1 |

empty set | 2 |

Functions | 6 |

Copyright | |

59 other sections not shown

### Common terms and phrases

algebra arbitrarily given assume Banach space bijective BM(E Boolean called Cauchy sequence closed sets closed subset completes the proof Consequently consider an arbitrary contains continuous function continuous linear operator converges define a function definition denote an arbitrary denote any point dense disjoint easily verify equivalent exists a natural exists a positive following corollary following proposition Frechet space function f Hausdorff space Hence we obtain Hilbert space holds homeomorphism iff there exists implies injective function inverse image isometric Lebesgue integrable Let X denote linear subspace locally compact measurable function measurable subset measure space metric space natural number neighborhood normed linear space open interval open set open subset outer measure positive real number pseudo-metric space pseudo-normed linear space real line remains to prove simple functions summable surjective function theorem topological group topological space topology vector