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Page 292
... uniform boundedness ( II.3.27 ) . Q.E.D. 8 LEMMA . Let Σ be a o - field of sets , E , a subfield of E determining the o - field Σ , and { u } a sequence of countably additive set functions de- fined on with values in a B - space X ...
... uniform boundedness ( II.3.27 ) . Q.E.D. 8 LEMMA . Let Σ be a o - field of sets , E , a subfield of E determining the o - field Σ , and { u } a sequence of countably additive set functions de- fined on with values in a B - space X ...
Page 383
... uniform con- vergence is sufficient to assure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he ...
... uniform con- vergence is sufficient to assure the continuity of the limit function . ( It is interesting that Weierstrass [ 1 ; p . 67 , 70 ] had employed this notion of convergence in some unpublished manuscripts written in 1841 - he ...
Page 857
... Uniform boundedness principle , in B - spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost periodic function , IV.7.4 ( 283 ) criterion for ...
... Uniform boundedness principle , in B - spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost periodic function , IV.7.4 ( 283 ) criterion for ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ