## Linear Operators: General theory |

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Page 195

with

with

**respect**to one variable and then with**respect**to the other , or vice versa . Indeed , according to Tonelli's theorem , both these integrals are equal to the integral off with**respect**to the product measure ( and we have already ...Page 306

The functions Mon are all continuous with

The functions Mon are all continuous with

**respect**to the measure defined by v ( un , E ) 2 ( E ) = Εε Σ . 2n i tulun , E ) ' and thus all belong to the subspace ca ( S , E , a ) consisting of all 2 - continuous functions in ca ( S , E ) ...Page 341

( ii ) There is a non - negative u in ba ( S , E ) with

( ii ) There is a non - negative u in ba ( S , E ) with

**respect**to which every 2 in K is continuous . ( iii ) lim , U = 1 uniformly with**respect**to 1 € K. 20 Let E = { En } be a countable field of subsets of a set S , and let & be the o ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero