## Topology and measure |

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### Contents

PART | 1 |

Basic result on construction of a measure | 3 |

Basic result on construction of an integral | 6 |

Copyright | |

16 other sections not shown

### Common terms and phrases

algebra Assume Baire sets Billingsley Borel bounded function Choose closed sets compact sets compact subset cone of functions Consider Construction of measures contains converges weakly convex cone countable base denote exists filtering finitely additive integral finitely additive measure follows function f functions X-»ft Furthermore GdK KcG given Hausdorff space holds indicator-functions inequality inf liminf inf limsup inf sup k<aj largest extension Lemma limsup Ma(f locally compact locally compact spaces mapping measure theory net-compact non-empty non-negative notes and remarks notion of convergence open sets points and closed positively homogeneous problem Prom proof of Theorem prove r-field Radon measures regular w.r.t. result Seiten semi-continuous sequence set function set-function defined simple functions subadditive sup inf sup liminf T-smooth T-smooth measure Theorem 2.2 tight and T-smooth tight content tight measures tion topological space vague topology Varadarajan weak convergence weak topology