## Linear Operators, Part 1 |

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Page 186

Thus the argument used in proving uniqueness in Lemma 1 goes through without

change in this case. Q.E.D. 3 DEFINITION. The

constructed in Theorem 2 is called the product

Thus the argument used in proving uniqueness in Lemma 1 goes through without

change in this case. Q.E.D. 3 DEFINITION. The

**measure space**(S, X, u)constructed in Theorem 2 is called the product

**measure space**of the**measure****spaces**...Page 188

E;) = II*(E), E, e 2, , and it follows from the uniqueness part of Theorem 2 for each

of the spaces (E9), 29), u0)), that u is the unique countably additive measure on 2

with this property. Q.E.D. As in the case of finite

E;) = II*(E), E, e 2, , and it follows from the uniqueness part of Theorem 2 for each

of the spaces (E9), 29), u0)), that u is the unique countably additive measure on 2

with this property. Q.E.D. As in the case of finite

**measure spaces**we shall call ...Page 405

sional Gauss

real sequences a = [al] as distinct from lo which is the subspace of s determined

by the condition X.1a* < x. The

...

sional Gauss

**measure**on the real line. The**space**s is, of course, the**space**of allreal sequences a = [al] as distinct from lo which is the subspace of s determined

by the condition X.1a* < x. The

**measure**as is countably additive; the subset le of...

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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