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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 §Åf ( x ) 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 §Åf ( x ) da depends only on the function f and the set A , and is independent of ...
Page 232
... integral equivalent to the Bochner integral . Somewhat more general integrals have been obtained for B - space va- lued functions by Birkhoff [ 4 ] , Gelfand [ 2 ] , Pettis [ 4 ] and Price [ 1 ] . Integrals for functions with values in ...
... integral equivalent to the Bochner integral . Somewhat more general integrals have been obtained for B - space va- lued functions by Birkhoff [ 4 ] , Gelfand [ 2 ] , Pettis [ 4 ] and Price [ 1 ] . Integrals for functions with values in ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ