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 f ( x ) da 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 ) da 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 . 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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ