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Page 3
... real function defined by the equations % ( s ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Sometimes , when the range of a transformation ƒ : A → B is to be emphasized at the expense of ƒ ... real numbers , I.1 3 NOTATION AND ELEMENTARY NOTIONS.
... real function defined by the equations % ( s ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Sometimes , when the range of a transformation ƒ : A → B is to be emphasized at the expense of ƒ ... real numbers , I.1 3 NOTATION AND ELEMENTARY NOTIONS.
Page 4
... real numbers , then the symbol lim sup A denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of the symbol lim inf A is similar . In particular , if A is a sequence ...
... real numbers , then the symbol lim sup A denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of the symbol lim inf A is similar . In particular , if A is a sequence ...
Page 11
... real numbers . Another base for this topology is obtained by taking a and b to be rational numbers . A subbase for this topology is given by all infinite intervals ( -∞ , a ) , ( b , + ∞ ) , where a and b are either real or rational ...
... real numbers . Another base for this topology is obtained by taking a and b to be rational numbers . A subbase for this topology is given by all infinite intervals ( -∞ , a ) , ( b , + ∞ ) , where a and b are either real or rational ...
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