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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 n + 1 \ f ( x ) − Σ F ...
... 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 n + 1 \ f ( x ) − Σ F ...
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
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