Linear Operators: General theory |
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Page 7
... belong to some subset E。€ 60 , and x ≤ y in the ordering of that E 。. It is clear that if ( UE , ' ) belongs to & it is an upper bound for &。. It will now be shown that it is well - ordered and hence belongs to ể . The statement x ...
... belong to some subset E。€ 60 , and x ≤ y in the ordering of that E 。. It is clear that if ( UE , ' ) belongs to & it is an upper bound for &。. It will now be shown that it is well - ordered and hence belongs to ể . The statement x ...
Page 184
... belong to A1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to and hence E. If the set function u is defined for Fe by the formula μ ( F ) ...
... belong to A1 . It follows that is closed under intersection and complementation and contains S. Thus is a field of sets . Moreover , each set of & belongs to and hence E. If the set function u is defined for Fe by the formula μ ( F ) ...
Page 350
... belongs to BV ( I ) if and only if it is the difference of two bounded monotone increasing functions defined on I. 74 Let ( S , Z , μ ) be a finite positive measure space . Show that an equivalent norm in the F - space TM ( S , Σ , μ ) ...
... belongs to BV ( I ) if and only if it is the difference of two bounded monotone increasing functions defined on I. 74 Let ( S , Z , μ ) be a finite positive measure space . Show that an equivalent norm in the F - space TM ( S , Σ , μ ) ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ