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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 Mn ) . We write and Σ = Σ Χ ... Χ Στ μ = μ.Χ ... Χμης ... 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 Mn ) . We write and Σ = Σ Χ ... Χ Στ μ = μ.Χ ... Χμης ... measure spaces ( Si , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
Page 405
... measure on the real line . The space s is , of course , the space of all real sequences a [ a ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset ↳1⁄2 of ...
... measure on the real line . The space s is , of course , the space of all real sequences a [ a ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset ↳1⁄2 of ...
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 { q1x } 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 { q1x } is dense in S ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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