## Linear Operators: General theory |

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Page 186

Thus, the field <P of Lemma 1 is a cr-field and the measure // of Lemma 1 is

countably additive on 0. ... The

is called the product

E ...

Thus, the field <P of Lemma 1 is a cr-field and the measure // of Lemma 1 is

countably additive on 0. ... The

**measure space**(S, E, p) constructed in Theorem 2is called the product

**measure space**of the**measure spaces**(Sn,En,fin). We writeE ...

Page 188

Q.E.D. As in the case of finite

S. E. p) constructed in Corollary 6 from the cr-finite

product

Q.E.D. As in the case of finite

**measure spaces**we shall call the**measure space**(S. E. p) constructed in Corollary 6 from the cr-finite

**measure spaces**(SjyEjtfif) theproduct

**measure space**and write (S,E,p) = P7-i (Si, zt,tii)- The best known ...Page 405

sional Gauss

real sequences x = [Xj] as distinct from l2, which is the subspace of s determined

by the condition 2JLi x^ < 00 □ The

sional Gauss

**measure**on the real line. The**space*** is, of course, the**space**of allreal sequences x = [Xj] as distinct from l2, which is the subspace of s determined

by the condition 2JLi x^ < 00 □ The

**measure**figo is countably additive; the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

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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 convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set 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 Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero