## Linear Operators: General theory |

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Page 341

Show that a set K C ba ( S , E ) is conditionally compact if and only if ( i ) K is

bounded . ... 22 Let S be a normal topological space and rca ( S ) the regular

countably additive set functions on the field of

S ) is ...

Show that a set K C ba ( S , E ) is conditionally compact if and only if ( i ) K is

bounded . ... 22 Let S be a normal topological space and rca ( S ) the regular

countably additive set functions on the field of

**Borel sets**in S . Prove that ( i ) rca (S ) is ...

Page 492

In the following , B denotes the field of

generated by the closed sets of S . If u is a function on B with values in a B -

space , then as in Definition IV . 10 . 3 , the symbol 14 ( E ) denotes the semi -

variation of u ...

In the following , B denotes the field of

**Borel sets**in S , i . e . , the o - fieldgenerated by the closed sets of S . If u is a function on B with values in a B -

space , then as in Definition IV . 10 . 3 , the symbol 14 ( E ) denotes the semi -

variation of u ...

Page 516

38 ( Markov ) Let S be a non - void set and $ a function on S to S . A function u

defined on the family of subsets of S is said ... negative measure u defined for all

38 ( Markov ) Let S be a non - void set and $ a function on S to S . A function u

defined on the family of subsets of S is said ... negative measure u defined for all

**Borel sets**in S with the properties that u is not identically zero and u is - invariant .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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