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 sÅf ( 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 sÅf ( 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 . 4 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914-924 ( 1951 ) . The generalized heat flow equation and a ...
... integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . 4 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914-924 ( 1951 ) . The generalized heat flow equation and a ...
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