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Page 3
... real function defined by the XE equations XE ( S ) = 1 , se E , and XE ( S ) = 0 , s ¢ E. : = = Sometimes , when the range of a transformation † : A → B is to be emphasized at the ... real numbers , I.1 3 NOTATION AND ELEMENTARY NOTIONS.
... real function defined by the XE equations XE ( S ) = 1 , se E , and XE ( S ) = 0 , s ¢ E. : = = Sometimes , when the range of a transformation † : A → B is to be emphasized at the ... 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 ...
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... 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 ( -∞o , a ) , ( b , + ∞∞ ) , where a and b are either real or ...
... 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 ( -∞o , a ) , ( b , + ∞∞ ) , where a and b are either real or ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ