Linear Operators: General theory |
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Page 7
... belong to some subset E。€ 80 , and x ≤ y in the ordering ≤ of that E 。. It is clear that if ( UE , ≤ ' ) belongs to & it is an upper bound for &。. It will now be shown that it is well - ordered and hence belongs to & . The ...
... belong to some subset E。€ 80 , and x ≤ y in the ordering ≤ of that E 。. It is clear that if ( UE , ≤ ' ) belongs to & it is an upper bound for &。. It will now be shown that it is well - ordered and hence belongs to & . The ...
Page 184
... belong to 1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to Ø and hence 2. If the set function u is defined for Fe by the formula μ ( F ) ...
... belong to 1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to Ø and hence 2. If the set function u is defined for Fe by the formula μ ( F ) ...
Page 355
... function g such that g ( s ) / s belongs to L1 and so ( g ( s ) / s ) ds = 1. If ƒ is integrable over any f finite interval , if and if lim toe - t * f ( x ) dz = A , t - 0 then tfo e - tz f ( z ) dz IV.13.93 355 EXERCISES.
... function g such that g ( s ) / s belongs to L1 and so ( g ( s ) / s ) ds = 1. If ƒ is integrable over any f finite interval , if and if lim toe - t * f ( x ) dz = A , t - 0 then tfo e - tz f ( z ) dz IV.13.93 355 EXERCISES.
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ