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Page 36
... vector space over a field Ø is an additive group together with an operation m : Þ × X written as m ( x , x ) = ax ... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → xx and ...
... vector space over a field Ø is an additive group together with an operation m : Þ × X written as m ( x , x ) = ax ... vector space are called vectors . The elements of the coefficient field are called scalars . The operations → xx and ...
Page 250
... vector in A has norm one and if every pair of distinct vectors in A are orthogonal . An orthonormal set is said to be complete if no non - zero vector is orthogonal to every vector in the set , i.e. , A is complete if { 0 } A. We recall ...
... vector in A has norm one and if every pair of distinct vectors in A are orthogonal . An orthonormal set is said to be complete if no non - zero vector is orthogonal to every vector in the set , i.e. , A is complete if { 0 } A. We recall ...
Page 795
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217–234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . 6. Some general theorems and convergence theorems in vector lattices ...
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217–234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . 6. Some general theorems and convergence theorems in vector lattices ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ