## Linear Operators: General theory |

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Page 262

Since the integral [ st ( s ) u ( ds )

Since the integral [ st ( s ) u ( ds )

**satisfies**the inequality | 1st ( 8 ) ( ds ) < sup | t ( s ) 0 ( yu , S ) , it is clear that the integral is a ...Page 495

Since B , is an algebra and

Since B , is an algebra and

**satisfies**condition ( ii ) , it is readily seen that B , is a o - field contained in B. We now show that B. B by proving that B ...Page 613

... the nonnegative real variable † which

... the nonnegative real variable † which

**satisfies**the functional equations f ... valued functions defined on the range t 2 0 , which**satisfy**the equations ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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