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Page 186
Thus the argument used in proving uniqueness in Lemma 1 goes through without
change in this case. Q.E.D. 3 DEFINITION. The measure space (S, X, u)
constructed in Theorem 2 is called the product measure space of the measure
spaces ...
Thus the argument used in proving uniqueness in Lemma 1 goes through without
change in this case. Q.E.D. 3 DEFINITION. The measure space (S, X, u)
constructed in Theorem 2 is called the product measure space of the measure
spaces ...
Page 188
E;) = II*(E), E, e 2, , and it follows from the uniqueness part of Theorem 2 for each
of the spaces (E9), 29), u0)), that u is the unique countably additive measure on 2
with this property. Q.E.D. As in the case of finite measure spaces we shall call ...
E;) = II*(E), E, e 2, , and it follows from the uniqueness part of Theorem 2 for each
of the spaces (E9), 29), u0)), that u is the unique countably additive measure on 2
with this property. Q.E.D. As in the case of finite measure spaces we shall call ...
Page 405
sional Gauss measure on the real line. The space s is, of course, the space of all
real sequences a = [al] as distinct from lo which is the subspace of s determined
by the condition X.1a* < x. The measure as is countably additive; the subset le of
...
sional Gauss measure on the real line. The space s is, of course, the space of all
real sequences a = [al] as distinct from lo which is the subspace of s determined
by the condition X.1a* < x. The measure as is countably additive; the subset le of
...
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Contents
A Settheoretic Preliminaries | 1 |
Convergence and Uniform Convergence of Generalized | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
27 other sections not shown
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Common terms and phrases
additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz 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 zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Nelson Dunford Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |