Linear Operators: General theory |
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Page 124
... sufficiently large k , and we may assume without loss of generality that ( h ( s ) v ( u , ds ) < 2ɛ for all k . By the simple form of the functions h the set n Ek = { sh ( s ) > v } is in for each y > 0. Moreover , yʊ ( μ , Ek ) ≤ f ̧ ...
... sufficiently large k , and we may assume without loss of generality that ( h ( s ) v ( u , ds ) < 2ɛ for all k . By the simple form of the functions h the set n Ek = { sh ( s ) > v } is in for each y > 0. Moreover , yʊ ( μ , Ek ) ≤ f ̧ ...
Page 414
... sufficiently small positive ɛ . It follows from the above that for some sufficiently small positive ɛ , q1 = r / ( 1 + ɛ ) + ɛp / ( 1 + ɛ ) is an interior point of K. Since q2 is a boundary point , it is not an internal point of K. But ...
... sufficiently small positive ɛ . It follows from the above that for some sufficiently small positive ɛ , q1 = r / ( 1 + ɛ ) + ɛp / ( 1 + ɛ ) is an interior point of K. Since q2 is a boundary point , it is not an internal point of K. But ...
Page 637
... sufficiently large t . On the other hand , we have seen that Y is integrable over every finite interval of the positive real axis . Thus , if we choose w1 sufficiently @ 1 large , So e - wit y ( t ) dt < ∞ . Consequently , by III.6.16 ...
... sufficiently large t . On the other hand , we have seen that Y is integrable over every finite interval of the positive real axis . Thus , if we choose w1 sufficiently @ 1 large , So e - wit y ( t ) dt < ∞ . Consequently , by III.6.16 ...
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