Linear Operators: General theory |
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Page 95
... valued function and ƒ a vector ( or scalar ) valued function . Thus , even if the integration process is defined with respect to a scalar valued set . function u , the resulting integral v may be a vector valued set function . It is ...
... valued function and ƒ a vector ( or scalar ) valued function . Thus , even if the integration process is defined with respect to a scalar valued set . function u , the resulting integral v may be a vector valued set function . It is ...
Page 224
... valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions ... valued analytic function of the complex variables 21 , ... , Zn , then a * f is a complex valued analytic function of 1 ...
... valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions ... valued analytic function of the complex variables 21 , ... , Zn , then a * f is a complex valued analytic function of 1 ...
Page 323
... valued measurable function ƒ is said to be integrable if there exists a sequence { f } of simple functions such that ( i ) fn ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the ... valued and μ IV.10.7 323 VECTOR VALUED MEASURES.
... valued measurable function ƒ is said to be integrable if there exists a sequence { f } of simple functions such that ( i ) fn ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the ... valued and μ IV.10.7 323 VECTOR VALUED MEASURES.
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ