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Page 186
... space ( S , 2 , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , En μn ) . We write and Σ = Σ Χ ... ΧΣ и = M1X ... XMn ... measure spaces ( Si , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
... space ( S , 2 , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , En μn ) . We write and Σ = Σ Χ ... ΧΣ и = M1X ... XMn ... measure spaces ( Si , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
Page 405
... space s is , of course , the space of all real sequences x = [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset la of s is of μ - measure zero ; the ...
... space s is , of course , the space of all real sequences x = [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset la of s is of μ - measure zero ; the ...
Page 725
... space , and let ( S , Σ , μ ) be a reg- ular finite measure space . Let p be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that P is met- rically transitive if and only if { q'x } is dense in S ...
... space , and let ( S , Σ , μ ) be a reg- ular finite measure space . Let p be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that P is met- rically transitive if and only if { q'x } is dense in S ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ