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Page 186
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 ..
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 measure spaces we shall call the measure space ( S , E , u ) constructed in ...
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 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 ...
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 ...
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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