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Page 387
... given by McShane [ 1 ] for a completely arbitrary measure space . A different proof in this context was given by J. Schwartz [ 1 ] . Generalizations of this theorem to the spaces of Orlicz were obtained by Zaanen [ 1 , 5 ; p . 138 ] ...
... given by McShane [ 1 ] for a completely arbitrary measure space . A different proof in this context was given by J. Schwartz [ 1 ] . Generalizations of this theorem to the spaces of Orlicz were obtained by Zaanen [ 1 , 5 ; p . 138 ] ...
Page 392
... given conditions assuring that a sequence of measurable functions has a uniformly convergent sub- sequence . ) Fréchet's arguments were simplified by Hanson [ 1 ] . Some- what different conditions have been given by Izumi [ 2 ] and ...
... given conditions assuring that a sequence of measurable functions has a uniformly convergent sub- sequence . ) Fréchet's arguments were simplified by Hanson [ 1 ] . Some- what different conditions have been given by Izumi [ 2 ] and ...
Page 729
... given by G. Birkhoff [ 7 ] and F. Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its adjoint , was given by Riesz and Sz . - Nagy [ 2 ] ...
... given by G. Birkhoff [ 7 ] and F. Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its adjoint , was given by Riesz and Sz . - Nagy [ 2 ] ...
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