## 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 , un ) . We write Σ = Σ , Χ ... ΧΣ ) , и1 х ... Хир » ( S , E , u ) = ( S1 , E1 , M7 ) X ..Page 188

It is clear that the measure has the property u ( P E ; ) II M ; ( E :) , Ε , ε Σ . , n ) - i = 1 ܕܐ and it follows from ... Q.E.D. As in the case of finite

It is clear that the measure has the property u ( P E ; ) II M ; ( E :) , Ε , ε Σ . , n ) - i = 1 ܕܐ and it follows from ... Q.E.D. As in the case of finite

**measure spaces**we shall call the**measure space**( S , E , u ) constructed in ...Page 405

sional Gauss

sional Gauss

**measure**on the real line . The**space**s is , of course , the**space**of all real sequences x [ x ] as distinct from le , which is the subspace of s determined by the condition 2x < .0 . The**measure**Moo is countably additive ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero