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Page 410
Nelson Dunford, Jacob T. Schwartz. 1 DEFINITION . A set KCX is convex if x , y e K , and 0 ≤ a ≤ 1 , imply ax + ( 1 ... CONVEX SETS AND WEAK TOPOLOGIES.
Nelson Dunford, Jacob T. Schwartz. 1 DEFINITION . A set KCX is convex if x , y e K , and 0 ≤ a ≤ 1 , imply ax + ( 1 ... CONVEX SETS AND WEAK TOPOLOGIES.
Page 414
... convex set K has at least one interior point p , an internal point 1 is an interior point , and a boundary point 2 is a bounding point . Since q is internal , the vector r = −εp + ( 1 + ε ) q , belongs to K for some sufficiently small ...
... convex set K has at least one interior point p , an internal point 1 is an interior point , and a boundary point 2 is a bounding point . Since q is internal , the vector r = −εp + ( 1 + ε ) q , belongs to K for some sufficiently small ...
Page 842
... Convex hull , Convex set , Convex space ) Convex function , definition , VI.10.1 ( 520 ) study of , VI.10 Convex hull , V.2.2 ( 414 ) Convex set , II.4.1 ( 70 ) definition , V.1.1 ( 410 ) study of , V.1-2 Convex space , locally , V.2.9 ...
... Convex hull , Convex set , Convex space ) Convex function , definition , VI.10.1 ( 520 ) study of , VI.10 Convex hull , V.2.2 ( 414 ) Convex set , II.4.1 ( 70 ) definition , V.1.1 ( 410 ) study of , V.1-2 Convex space , locally , V.2.9 ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ