Linear Operators: General theory |
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Page 232
... scalar valued measure . The possibility of extending the integral to this realm was recognized by L. M. Graves [ 3 ] , who discussed and applied the Riemann integral . A theory of the Lebesgue type was constructed by Bochner [ 2 ] . The ...
... scalar valued measure . The possibility of extending the integral to this realm was recognized by L. M. Graves [ 3 ] , who discussed and applied the Riemann integral . A theory of the Lebesgue type was constructed by Bochner [ 2 ] . The ...
Page 233
... type theory of integration of a scalar function with respect to a countably additive vector valued measure . Instances in which both the function and the measure are vector valued have also been considered by Bochner and Taylor [ 1 ; pp ...
... type theory of integration of a scalar function with respect to a countably additive vector valued measure . Instances in which both the function and the measure are vector valued have also been considered by Bochner and Taylor [ 1 ; pp ...
Page 391
... scalar valued cases to the ordinary total variation . In an abstract case , it was employed by Gowurin [ 1 ] who developed a Riemann - type ... type theory of integration of a scalar valued func- tion with respect to a vector valued measure ...
... scalar valued cases to the ordinary total variation . In an abstract case , it was employed by Gowurin [ 1 ] who developed a Riemann - type ... type theory of integration of a scalar valued func- tion with respect to a vector valued measure ...
Contents
Preliminary Concepts | 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 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