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Page 125
... sufficiently large n . Hence f - fnp < 28 for sufficiently large n and the proof is complete . Q.E.D. 4. Countably Additive Set Functions The basis for the present III.3.8 125 LEBESGUE SPACES.
... sufficiently large n . Hence f - fnp < 28 for sufficiently large n and the proof is complete . Q.E.D. 4. Countably Additive Set Functions The basis for the present III.3.8 125 LEBESGUE SPACES.
Page 592
... sufficiently near 2 , the inverse T - 1 ( 2 ) exists and is an analytic function of 2 in a neighborhood of 20. To prove the second part of the lemma we suppose that there is a number 26 in D and a sequence { m } CD such that leσ ( T ...
... sufficiently near 2 , the inverse T - 1 ( 2 ) exists and is an analytic function of 2 in a neighborhood of 20. To prove the second part of the lemma we suppose that there is a number 26 in D and a sequence { m } CD such that leσ ( T ...
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 w , sufficiently @ 1 large , 00 Š e - wit y ( t ) dt < ∞ . Consequently , by III ...
... 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 w , sufficiently @ 1 large , 00 Š e - wit y ( t ) dt < ∞ . Consequently , by III ...
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ