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Page 95
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... DEFINITION . A set function μ defined on a 95 Integration and Set Functions.
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... DEFINITION . A set function μ defined on a 95 Integration and 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 dλ / du is defined ... function μ on Σ the equation μ ( þ ̃1 ( E ) ) = μ2 ( 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 dλ / du is defined ... function μ on Σ the equation μ ( þ ̃1 ( E ) ) = μ2 ( E ) defines an additive set ...
Page 223
... function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = ag ( 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 = ag ( 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
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ