## 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

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

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

**integral**theorem states : If we agree to orient the Jordan ... 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 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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