Linear Operators: General theory |
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Page 10
... sets in 7 are called the open sets of ( X , t ) . A neighborhood of the point p is an open set containing p . A neighborhood of the set A is an open set containing A. If A is a subset of X , then a point p is a limit point , or a point ...
... sets in 7 are called the open sets of ( X , t ) . A neighborhood of the point p is an open set containing p . A neighborhood of the set A is an open set containing A. If A is a subset of X , then a point p is a limit point , or a point ...
Page 84
... open set onto a set whose closure contains an open set . Pettis [ 5 ] proved theorems extending some of the results of Banach [ 7 ] , Freudenthal [ 2 ] , and Lorentz [ 3 ] , and which , when spe- cialized to linear spaces , contain most ...
... open set onto a set whose closure contains an open set . Pettis [ 5 ] proved theorems extending some of the results of Banach [ 7 ] , Freudenthal [ 2 ] , and Lorentz [ 3 ] , and which , when spe- cialized to linear spaces , contain most ...
Page 213
... open set G of real Euclidean n - space En . Let 0 < r < ∞ . ( a ) If for each p in a set ACG 2 ( C ) lim inf μ ( C ) → 0 μ ( C ) < r , where C is a closed cube containing p , then each neighborhood of A con- tains an open set Q such ...
... open set G of real Euclidean n - space En . Let 0 < r < ∞ . ( a ) If for each p in a set ACG 2 ( C ) lim inf μ ( C ) → 0 μ ( C ) < r , where C is a closed cube containing p , then each neighborhood of A con- tains an open set Q such ...
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