Linear Operators: General theory |
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Page 143
... Borel measure in [ a , b ] . The Lebesgue measurable sets in [ a , b ] are the sets in the Lebesgue extension ( relative to Borel measure ) of the o - field of Borel sets in [ a , b ] . Similarly , the Lebesgue - Stieltjes measure ...
... Borel measure in [ a , b ] . The Lebesgue measurable sets in [ a , b ] are the sets in the Lebesgue extension ( relative to Borel measure ) of the o - field of Borel sets in [ a , b ] . Similarly , the Lebesgue - Stieltjes measure ...
Page 492
... Borel sets in E and all finite sets of scalars α1 , ... , an with α , ≤ 1 . We are now prepared to represent the general operator . 2 THEOREM . Let S be a compact Hausdorff space and let T be an operator on C ( S ) to X. Then there ...
... Borel sets in E and all finite sets of scalars α1 , ... , an with α , ≤ 1 . We are now prepared to represent the general operator . 2 THEOREM . Let S be a compact Hausdorff space and let T be an operator on C ( S ) to X. Then there ...
Page 516
... Borel sets of S which is not identically zero and is 4 - invariant for every e G. n - 1 42 Show that in Exercise 38 the set function u is unique up to a positive constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to ...
... Borel sets of S which is not identically zero and is 4 - invariant for every e G. n - 1 42 Show that in Exercise 38 the set function u is unique up to a positive constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ