## Linear Operators: General theory |

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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**So 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 ...### What people are saying - Write a review

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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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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