## Linear Operators: General theory |

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Page 341

Show that a set KC 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 KC 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 lu | ( 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 lu | ( 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 A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 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 analytic applied arbitrary assumed B-space ba(S Borel bounded called Chapter clear closed compact complex condition Consequently constant contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hausdorff Hence Hilbert space identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear space mapping Math means measure space neighborhood norm obtained operator positive measure preceding projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero