## Linear Operators: General theory |

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Page 186

Thus, the field 0 of Lemma 1 is a a-field and the measure (i of Lemma 1 is

countably additive on 0. Consequently ... The

constructed in Theorem 2 is called the product

Thus, the field 0 of Lemma 1 is a a-field and the measure (i of Lemma 1 is

countably additive on 0. Consequently ... The

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

**measure space**of the**measure****spaces**(Sn, E„, fin).Page 188

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

S, E, (i) 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, (i) constructed in Corollary 6 from the cr-finite

**measure spaces**(Sit Et, fa) theproduct

**measure space**and write (S, E, fi) = P?-i(SitE{,fa). The best known ...Page 405

sional Gauss

real sequences x = as distinct from which is the subspace of * determined by the

condition 2^2^ < 00 • The

sional Gauss

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

condition 2^2^ < 00 • The

**measure**fioc is countably additive; the subset ^ of s is ...### 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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