Linear Operators: General theory |
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Page 195
... integral of ƒ with respect to the product measure ( and we have already remarked that the product of measures is com- mutative . ) Generalizing this statement , and making use of the com- mutativity and associativity of product measures ...
... integral of ƒ with respect to the product measure ( and we have already remarked that the product of measures is com- mutative . ) Generalizing this statement , and making use of the com- mutativity and associativity of product measures ...
Page 227
... integral theorem states : If we agree to orient the Jordan curves comprising B in the positive sense customary in the theory of complex variables , then §Âf ( a ) da depends only on the function f and the set A , and is independent of ...
... integral theorem states : If we agree to orient the Jordan curves comprising B in the positive sense customary in the theory of complex variables , then §Âf ( a ) da depends only on the function f and the set A , and is independent of ...
Page 743
... integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914–924 ( 1951 ) . The generalized heat flow equation and a corresponding ...
... integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914–924 ( 1951 ) . The generalized heat flow equation and a corresponding ...
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