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Page 96
... symmetric difference ( A – B ) ○ ( B — A ) . 3 DEFINITION . Let S be a set . A field of subsets of S , or a Boolean algebra of subsets of S , is a non - empty family of subsets of S which contains the null set , the complement ...
... symmetric difference ( A – B ) ○ ( B — A ) . 3 DEFINITION . Let S be a set . A field of subsets of S , or a Boolean algebra of subsets of S , is a non - empty family of subsets of S which contains the null set , the complement ...
Page 156
... symmetric difference ( AE ) -AE of A and E. The fact that is an equivalence relation follows readily from the fact that the symmetric difference is a commutative and associative operation with AAA = 6. The set ( u ) of all equivalence ...
... symmetric difference ( AE ) -AE of A and E. The fact that is an equivalence relation follows readily from the fact that the symmetric difference is a commutative and associative operation with AAA = 6. The set ( u ) of all equivalence ...
Page 813
... symmetric operator . Doklady Akad . Nauk SSSR ( N. S. ) 71 , 241-244 ( 1950 ) . ( Russian ) Math . Rev. 11 , 600 ( 1950 ) . Generalized resolvents of symmetric operators . Izvestiya Akad . Nauk SSSR Ser . Mat . 18 , 51-86 ( 1954 ) ...
... symmetric operator . Doklady Akad . Nauk SSSR ( N. S. ) 71 , 241-244 ( 1950 ) . ( Russian ) Math . Rev. 11 , 600 ( 1950 ) . Generalized resolvents of symmetric operators . Izvestiya Akad . Nauk SSSR Ser . Mat . 18 , 51-86 ( 1954 ) ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ