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Page 44
... B is a Boolean algebra and xv y = x + y + xy , xy , and x ' хлу = xy . 1 + x Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : B → C , then h is said to be a ...
... B is a Boolean algebra and xv y = x + y + xy , xy , and x ' хлу = xy . 1 + x Thus the concepts of Boolean algebra and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : B → C , then h is said to be a ...
Page 396
... algebra , norm and order properties . Further results based only on algebra and norm properties were developed by Gelfand [ 1 ] in the complex case and were ... algebraic considerations are for 396 IV.16 IV . SPECIAL SPACES B-Algebras.
... algebra , norm and order properties . Further results based only on algebra and norm properties were developed by Gelfand [ 1 ] in the complex case and were ... algebraic considerations are for 396 IV.16 IV . SPECIAL SPACES B-Algebras.
Page 495
... B and if f ( s ) : lim , fn ( s ) for every s in S , then fe B. 8 个 0 - = It is evident that Bo possesses these two properties . We now prove that Bo is an algebra under the natural product ( fg ) ( s ) f ( s ) g ( s ) , s € S. To see ...
... B and if f ( s ) : lim , fn ( s ) for every s in S , then fe B. 8 个 0 - = It is evident that Bo possesses these two properties . We now prove that Bo is an algebra under the natural product ( fg ) ( s ) f ( s ) g ( s ) , s € S. To see ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ