Linear Operators: General theory |
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Page 186
... space ( S , E , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , En n ) . We write Σ - ΣΧ ... ΧΣτ μ M1X ... XMп , and ( S ... measure spaces ( S1 , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
... space ( S , E , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , En n ) . We write Σ - ΣΧ ... ΧΣτ μ M1X ... XMп , and ( S ... measure spaces ( S1 , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
Page 347
... measure or a null set . n = 1 50 Show that no space equivalent to a space C ( S ) is equivalent to a closed subspace of a space ba ( S , 2 ) unless both are finite dimen- sional . 51 Show that no space L , ( S , Σ , μ ) , 1 < p ...
... measure or a null set . n = 1 50 Show that no space equivalent to a space C ( S ) is equivalent to a closed subspace of a space ba ( S , 2 ) unless both are finite dimen- sional . 51 Show that no space L , ( S , Σ , μ ) , 1 < p ...
Page 405
... space s is , of course , the space of all real sequences a [ x ] as distinct from l2 , which is the subspace of s determined by the condition Σ < ∞o . The measure His countably additive ; the subset l2 of s is of μ - measure zero ; the ...
... space s is , of course , the space of all real sequences a [ x ] as distinct from l2 , which is the subspace of s determined by the condition Σ < ∞o . The measure His countably additive ; the subset l2 of s is of μ - measure zero ; the ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ