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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 ( relative ...
... 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 ( relative ...
Page 156
... symmetric difference ( A ○ E ) — 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 ...
... symmetric difference ( A ○ E ) — 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 ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ