## 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 Gf of X * such that each f € 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 = $ + ( x ) . The flow is assumed to have the property that ( i ) pe ( $ ( x ) ) = 0t + 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 | |

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