## Linear Operators: General theory |

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Page 186

The

The

**measure space**( S , E , u ) constructed in Theorem 2 is called the product**measure space**of the**measure spaces**( Sn , En , Mm ) . We write Σ = Σ , Χ ... ΧΣ » U = My X ... X Mony ( S , Σ , μ ) = ( SI , ΣΙ , μ ) x ... x ( S ,, Ση , μη ) ...Page 188

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

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

**measure spaces**we shall call the**measure space**( S , E , M ) constructed in Corollary 6 from the o - finite**measure spaces**( Si , Eie Mi ) the product**measure space**and write ( S , E , u ) P - 1 ( Si ...Page 849

... VI.9.28 ( 515 ) Maximal element , Hausdorff maximality theorem , 1.2.6 ( 6 ) in a partially ordered

... VI.9.28 ( 515 ) Maximal element , Hausdorff maximality theorem , 1.2.6 ( 6 ) in a partially ordered

**space**, 1.2.4 ( 4 ) ... linear**space**, III.9.7 ( 169 ) , III.9.28 ( 171 )**Measurable**set , definition , III.4.3 ( 126 )**Measure**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero