Linear Operators: General theory |
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Page 143
... measure on as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue ...
... measure on as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue ...
Page 186
... measure with the desired properties . To prove the uniqueness of u , we note that it follows in the same way that ... measure space ( S , 2 , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
... measure with the desired properties . To prove the uniqueness of u , we note that it follows in the same way that ... measure space ( S , 2 , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
Page 405
... measure zero ; the measure μ is not countably additive . In fact , using the relation between Моо and Ма it is easy to see that l is the union of a countable family of u - null sets . These relationships may be summed up in the ...
... measure zero ; the measure μ is not countably additive . In fact , using the relation between Моо and Ма it is easy to see that l is the union of a countable family of u - null sets . These relationships may be summed up in the ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ