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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 2 = Σ Χ ... ΧΣτ Σ ( S , E , μ ) = ( S1 ... measure spaces ( Si , 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 2 = Σ Χ ... ΧΣτ Σ ( S , E , μ ) = ( S1 ... 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 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 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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite 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 theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ