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Page 164
... non - negative set function on to Σ is non - negative , it follows that { un ( E ) } is a bounded non - decreasing set of real numbers for each E € 21 . We define λ1 ( E ) lim , ( E ) , E e 21. By Corollary 4 , 21 is countably additive ...
... non - negative set function on to Σ is non - negative , it follows that { un ( E ) } is a bounded non - decreasing set of real numbers for each E € 21 . We define λ1 ( E ) lim , ( E ) , E e 21. By Corollary 4 , 21 is countably additive ...
Page 179
... non- negative μ - measurable function defined on S and 2 ( E ) = f ( s ) u ( ds ) , ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √ ̧g ( s ) λ ( ds ) = √¿ † ( s ) g ( s ) μ ( ds ) ...
... non- negative μ - measurable function defined on S and 2 ( E ) = f ( s ) u ( ds ) , ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √ ̧g ( s ) λ ( ds ) = √¿ † ( s ) g ( s ) μ ( ds ) ...
Page 516
... non - negative measure μ defined for all Borel sets in S with the prop- erties that is not identically zero and u is o - invariant . 40 Let S be a non - void set and G a family of functions on S to S. Suppose that 41 ( 42 ( 8 ) ) = 42 ...
... non - negative measure μ defined for all Borel sets in S with the prop- erties that is not identically zero and u is o - invariant . 40 Let S be a non - void set and G a family of functions on S to S. Suppose that 41 ( 42 ( 8 ) ) = 42 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ