## Linear Operators, Part 1 |

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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 f with respect to the product measure (and we have already remarkedthat the product of measures is commutative.) Generalizing this statement, and ...

Page 227

Then the second form of Cauchy's

the Jordan curves comprising B in the positive sense customary in the theory of

complew variables, then saf(z)dz depends only on the function f and the set A,

and ...

Then the second form of Cauchy's

**integral**theorem states: If we agree to orientthe Jordan curves comprising B in the positive sense customary in the theory of

complew variables, then saf(z)dz depends only on the function f and the set A,

and ...

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

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero