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 งลƒ ( α ) 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 งลƒ ( α ) 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 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914-924 ( 1951 ) . 3. The generalized heat flow equation and a corresponding ...
... integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . The first variation of an indefinite Wiener integral . Proc . Amer . Math . Soc . 2 , 914-924 ( 1951 ) . 3. The generalized heat flow equation and a corresponding ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ