## Linear Operators: General theory |

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that is , for every a € A , the

that is , for every a € A , the

**function f**assigns an element f ( a ) € B. If f : A + B and g : B → C , then the mapping gf : A → C is defined by the ...Page 196

For each s in S , F ( s ) is an equivalence class of functions , any pair of whose ... If for each s we select a particular

For each s in S , F ( s ) is an equivalence class of functions , any pair of whose ... If for each s we select a particular

**function f**( s , :) € F ( s ) ...Page 199

integral Ss ( s , t ) u ( ds ) , as a

integral Ss ( s , t ) u ( ds ) , as a

**function of**t , is equal to the element Ss F ( s ) q ( ds ) of L , ( T , ET , 2 , X ) . Proof .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero