Linear Operators: General theory |
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Page 10
... sets in 7 are called the open sets of ( X , 7 ) . 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 , 7 ) . 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
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ