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Page 177
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { s \ s e F , f ( s ) ≤ n } . Then F = F and v ( λ , F2 ) ...
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { s \ s e F , f ( s ) ≤ n } . Then F = F and v ( λ , F2 ) ...
Page 278
... assumed that x * = x * f . Then there is a point s in S such that x * f = f ( s ) , fe C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to a ...
... assumed that x * = x * f . Then there is a point s in S such that x * f = f ( s ) , fe C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to a ...
Page 657
... assumed to be governed by the classical Hamiltonian equations and so is subject to a principle of scientific determinism whereby it is known that an initial state a will , after t seconds have elapsed , have passed into a uniquely ...
... assumed to be governed by the classical Hamiltonian equations and so is subject to a principle of scientific determinism whereby it is known that an initial state a will , after t seconds have elapsed , have passed into a uniquely ...
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