## Linear Operators: General theory |

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Page 195

Indeed, according to Tonelli's theorem, both these

that the product of measures is commutative.) Generalizing this statement, and ...

Indeed, according to Tonelli's theorem, both these

**integrals**are equal to the**integral**of / with respect to the product measure (and we have already remarkedthat the product of measures is commutative.) Generalizing this statement, and ...

Page 227

Let / be analytic in V—A. Then the second form of Cauchy's

states: // we agree to orient the Jordan curves ... and is independent of any

particular choice of the neighborhood U of A. In other words, the

J"Bi are ...

Let / be analytic in V—A. Then the second form of Cauchy's

**integral**theoremstates: // we agree to orient the Jordan curves ... and is independent of any

particular choice of the neighborhood U of A. In other words, the

**integrals**JB andJ"Bi are ...

Page 232

The possibility of extending the

Graves [3], who discussed and applied the Riemann

Lebesgue type was constructed by Bochner [2]. The Cauchy sequence method of

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 theLebesgue type was constructed by Bochner [2]. The Cauchy sequence method of

the ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 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

a-finite Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space valued function vector space weak topology weakly compact weakly sequentially compact zero