## Linear Operators, Part 1 |

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Page 136

There is a uniquely

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 . The

intersection ...

There is a uniquely

**determined**smallest field and a uniquely**determined**smallesto - 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 . The

intersection ...

Page 455

Let G = U_Yn ; then f is

subset of X * , there exists a denumerable subset Gf of X * such that each f € F is

can be ...

Let G = U_Yn ; then f is

**determined**by G. It follows that if F is a denumerablesubset 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 functional |can be ...

Page 657

... after t seconds have elapsed , have passed into a uniquely

state y . Since y is uniquely

defined by the equation y = $ + ( x ) . The flow is assumed to have the property

that ( i ) ...

... after t seconds have elapsed , have passed into a uniquely

**determined**newstate y . Since y is uniquely

**determined**by x and t , a function be on S to S isdefined by the equation y = $ + ( x ) . The flow is assumed to have the property

that ( i ) ...

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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