Linear Operators: General theory |
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Page 195
... integral off 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 off 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 f ( x ) dx depends only on the function f and the set A , and is independent of any ...
... 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 f ( x ) dx depends only on the function f and the set A , and is independent of any ...
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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ