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... T. Schwartz Vol . VIII : Modern Geometrical Optics By Max Herzberger Vol . IX : Orthogonal Expansions By G. Sansone Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Preliminary Concepts.
... T. Schwartz Vol . VIII : Modern Geometrical Optics By Max Herzberger Vol . IX : Orthogonal Expansions By G. Sansone Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs Preliminary Concepts.
Page 16
... applying to the pair f1 , μ1 the procedure applied to fo , Mo , and then continuing inductively , one obtains a sequence F1 , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and n \ f ( x ) − Σ F , ( x ) ...
... applying to the pair f1 , μ1 the procedure applied to fo , Mo , and then continuing inductively , one obtains a sequence F1 , i = 1 , 2 , . . . , of real continuous functions on X , with the properties : and n \ f ( x ) − Σ F , ( x ) ...
Page 81
... applied these results to a large number of special spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by Hildebrandt [ 2 ] in the case of a B - space . Banach and Steinhaus [ 1 ; p , 53 ] observed that in the ...
... applied these results to a large number of special spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by Hildebrandt [ 2 ] in the case of a B - space . Banach and Steinhaus [ 1 ; p , 53 ] observed that in the ...
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