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Page 48
... equivalent to the well - ordering principle ( as in Theorem 2.6 ) is in Hausdorff [ 1 ; p . 140 ] . Zorn [ 1 ] gave a theorem essentially equivalent to Theorem 2.7 . A similar theorem is due to R. L. Moore [ 1 ; p . 84 ] . For proofs of ...
... equivalent to the well - ordering principle ( as in Theorem 2.6 ) is in Hausdorff [ 1 ; p . 140 ] . Zorn [ 1 ] gave a theorem essentially equivalent to Theorem 2.7 . A similar theorem is due to R. L. Moore [ 1 ; p . 84 ] . For proofs of ...
Page 91
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
... equivalent metric . See also van Dantzig [ 1 ] , [ 2 ] . Norms in linear spaces . We have seen that in a normed ... equivalent invariant metric , but that an F - space may have no bounded sphere . Eidelheit and Mazur [ 1 ] have proved ...
Page 347
... equivalent to a closed subspace of a space ba ( S , E ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 4 ) , unless it is ...
... equivalent to a closed subspace of a space ba ( S , E ) unless both are finite dimen- sional . 51 Show that no space L „ ( S , Σ , μ ) , 1 < p < ∞ , is equivalent either to a space C ( S ) or a space L1 ( S1 , E1 , 4 ) , unless it is ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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