## Linear Operators: General theory |

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Page 136

There is a uniquely

There is a uniquely

**determined**smallest field and a uniquely**determined**smallest o - field containing a given family of sets . Proof . There is at least one field , namely the field of all subsets of S , which contains a given family t ...Page 455

Let G = U_Yn ; then f is

Let G = U_Yn ; then f is

**determined**by G. It follows that if F is a denumerable subset of X * , there exists a denumerable subset G , of X * such that each f e F is**determined**by GF We can even assert that each continuous linear ...Page 657

Since y is uniquely

Since y is uniquely

**determined**by x and t , a function be on S to S is defined by the equation y = 0. ( x ) . The flow , is assumed to have the property that ( i ) di ( ar ) ) = $ e + s ( x ) , for all points x in phase space and for ...### 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 | |

91 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 closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero