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Page 125
... sufficiently large n . Hence \ f - fn \ p < 2ɛ 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 - fn \ p < 2ɛ 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 a sufficiently large , Consequently , by III.6.16 , e - wity ( t ) dt < ∞ . lim fo ...
... 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 a sufficiently large , Consequently , by III.6.16 , e - wity ( t ) dt < ∞ . lim fo ...
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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ