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Page vi
... present work is written for the student as well as for the mature mathematician . Much of the text has grown directly out of lec- tures given by the authors over many years , and the two parts are de- signed to form suitable texts for a ...
... present work is written for the student as well as for the mature mathematician . Much of the text has grown directly out of lec- tures given by the authors over many years , and the two parts are de- signed to form suitable texts for a ...
Page 285
... present theorem is a corollary of Theorem 6.18 . Q.E.D. 8. The Spaces L „ ( S , Σ , μ ) The spaces L , ( S , Σ , μ ) , 1 ≤ p < ∞ , have already been studied in Chapter III . In particular it was shown in Theorem III.6.6 that they are ...
... present theorem is a corollary of Theorem 6.18 . Q.E.D. 8. The Spaces L „ ( S , Σ , μ ) The spaces L , ( S , Σ , μ ) , 1 ≤ p < ∞ , have already been studied in Chapter III . In particular it was shown in Theorem III.6.6 that they are ...
Page 286
... present , that μ ( S ) < ∞o . If XE is the characteristic function of the set E e E , then , if { E } is a disjoint sequence of measurable subsets of S and UE ; Eg , it follows from III.6.16 that - = 1 ZE , = XE 。' Σ j = 1 00 the ...
... present , that μ ( S ) < ∞o . If XE is the characteristic function of the set E e E , then , if { E } is a disjoint sequence of measurable subsets of S and UE ; Eg , it follows from III.6.16 that - = 1 ZE , = XE 。' Σ j = 1 00 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