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Page 95
... function , complex function , etc. , where the adjectives real and complex ... defined with respect to a scalar valued set function μ , the resulting ... Functions 95 35 Finitely Additive Set Functions.
... function , complex function , etc. , where the adjectives real and complex ... defined with respect to a scalar valued set function μ , the resulting ... Functions 95 35 Finitely Additive Set Functions.
Page 182
... function f of Theorems 2 and 7 is called the Radon - Nikodým derivative of 2 with respect to μ and is often denoted by dλ / du . Thus da / du is defined ... function μ on Σ the equation μ ( −1 ( E ) ) = μ1⁄2 ( E ) defines an additive set ...
... function f of Theorems 2 and 7 is called the Radon - Nikodým derivative of 2 with respect to μ and is often denoted by dλ / du . Thus da / du is defined ... function μ on Σ the equation μ ( −1 ( E ) ) = μ1⁄2 ( E ) defines an additive set ...
Page 223
... function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = Sag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) = b . Show that the Lebesgue ...
... function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = Sag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) = b . Show that the Lebesgue ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ