## 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 , x ... ΧΣη » μ = μ . Χ ... Χμη , ( S , E , y ) = ( S1 , E1 , M2 ) .Page 188

It is clear that the measure has the property n n MC PE ; ) = I1 M : ( E . ) , Ε , ε Σ . , and it follows from the ... Q.E.D. As in the case of finite

It is clear that the measure has the property n n MC PE ; ) = I1 M : ( E . ) , Ε , ε Σ . , and it follows from the ... Q.E.D. As in the case of finite

**measure spaces**we shall call the**measure space**( S , E , u ) constructed in Corollary ...Page 849

as study of TM , IV.11 , IV.15 a topological linear

as study of TM , IV.11 , IV.15 a topological linear

**space**, 111.9.7 ( 169 ) , III.9.28 ( 171 )**Measurable**set , definition , III.4.3 ( 126 )**Measure**. ( See also Set function ) Borel or Borel - Lebesgue , ( 139 ) Borel - Stieltjes ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero