## Linear Operators: General theory |

### From inside the book

Results 1-3 of 85

Page 195

Indeed , according to Tonelli's theorem , both these

Indeed , according to Tonelli's theorem , both these

**integrals**are equal to the**integral**off with respect to the product measure ( and we have already remarked that the product of measures is commutative . ) Generalizing this statement ...Page 227

Let f be analytic in V - A . Then the second form of Cauchy's

Let f be analytic in V - A . Then the second form of Cauchy's

**integral**theorem states : If we agree to orient the ... and is independent of any particular choice of the neighborhood U of A. In other words , the**integrals**SB and SB ...Page 232

The possibility of extending the

The possibility of extending the

**integral**to this realm was recognized by L. M. Graves 3 ] , who discussed and applied the Riemann**integral**. A theory of the Lebesgue type was constructed by Bochner [ 2 ] . The Cauchy sequence method of ...### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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