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Page 440
... q . Then , by 2.13 , there is a functional a * € X * such that Rx * ( p ) ‡ Rx * ( q ) . This implies that A1 = { xx ... Let K be a subset of a linear space , let A1 be an extremal subset of K , and A , an extremal subset of A1 . Then A ...
... q . Then , by 2.13 , there is a functional a * € X * such that Rx * ( p ) ‡ Rx * ( q ) . This implies that A1 = { xx ... Let K be a subset of a linear space , let A1 be an extremal subset of K , and A , an extremal subset of A1 . Then A ...
Page 442
... let gne C ( Q ) be such that gn≤1 / n , gn ( P ) = 0 for p Nn , and gn ( p ) = x1 ( p ) for pe M. Then X1gn → X1 , x - gn≤ 1 , and a1 - g , vanishes in M. It follows that y * ( x1 ) = * ( x ) = 0. If xe C ( Q ) is such that x ( q ) 0 ...
... let gne C ( Q ) be such that gn≤1 / n , gn ( P ) = 0 for p Nn , and gn ( p ) = x1 ( p ) for pe M. Then X1gn → X1 , x - gn≤ 1 , and a1 - g , vanishes in M. It follows that y * ( x1 ) = * ( x ) = 0. If xe C ( Q ) is such that x ( q ) 0 ...
Page 725
... Let S be a compact metric space , and let ( S , Σ , μ ) be a reg- ular finite measure space . Let be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that q is met- rically transitive if and only if { ...
... Let S be a compact metric space , and let ( S , Σ , μ ) be a reg- ular finite measure space . Let be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that q is met- rically transitive if and only if { ...
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