## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 97

Page 136

Nelson Dunford, Jacob T. Schwartz, William

LEMMA . There is a uniquely determined smallest

determined smallest o -

least one ...

Nelson Dunford, Jacob T. Schwartz, William

**G**. Bade, Robert**G**. Bartle. и аn 6LEMMA . There is a uniquely determined smallest

**field**and a uniquelydetermined smallest o -

**field**containing a given family of sets . Proof . There is atleast one ...

Page 137

Nelson Dunford, Jacob T. Schwartz, William

and ... The smallest o -

space S is called the Borel

Nelson Dunford, Jacob T. Schwartz, William

**G**. Bade, Robert**G**. Bartle. its realand ... The smallest o -

**field**B containing all the closed sets of a given topologicalspace S is called the Borel

**field**of S , and the sets in B are called the Borel sets .Page 169

Suppose that the

Show that L ( S , E , u , X ) is separable if the B - space X is separable . 7 Show

that F ( S ) need not be a linear topological space if u is not bounded , nor if u is ...

Suppose that the

**field**Eis separable under the metric**g**( E , F ) = v ( u , E A F ) .Show that L ( S , E , u , X ) is separable if the B - space X is separable . 7 Show

that F ( S ) need not be a linear topological space if u is not bounded , nor if u is ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Other editions - View all

### 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