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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 414
... sufficiently small positive & . It follows from the above that for some sufficiently small positive ε , q1 = r / ( 1 + e ) + εp / ( 1 + ɛ ) is an interior point of K. Since 42 is a boundary point , it is not an internal point of K. But ...
... sufficiently small positive & . It follows from the above that for some sufficiently small positive ε , q1 = r / ( 1 + e ) + εp / ( 1 + ɛ ) is an interior point of K. Since 42 is a boundary point , it is not an internal point of K. But ...
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 λ in D and a sequence { m } CD such that leσ ( T ( 2m ) ...
... 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 λ in D and a sequence { m } CD such that leσ ( T ( 2m ) ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ