Linear Operators: General theory |
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Page 241
... Remark . In Chapter III the space L , ( S , Σ , μ ) was defined without the assumption that u is non - negative ... Remark . In defining the following four spaces the term interval is used for a set of real numbers having any one of the ...
... Remark . In Chapter III the space L , ( S , Σ , μ ) was defined without the assumption that u is non - negative ... Remark . In defining the following four spaces the term interval is used for a set of real numbers having any one of the ...
Page 838
... remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - space ( or ...
... remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compact- ness of continuous functions , IV.6.7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - space ( or ...
Page 844
... remarks on , ( 728-730 ) Essential least upper bound , definition III.1.11 ( 100–101 ) Essential singularity , definition ... remark on , ( 88 ) Fatou theorem , on limits and integrals , III.6.19 ( 152 ) , III.9.35 ( 172 ) Field , in ...
... remarks on , ( 728-730 ) Essential least upper bound , definition III.1.11 ( 100–101 ) Essential singularity , definition ... remark on , ( 88 ) Fatou theorem , on limits and integrals , III.6.19 ( 152 ) , III.9.35 ( 172 ) Field , in ...
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