Linear Operators, Part 1 |
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Page 136
There is a uniquely determined smallest field and a uniquely determined smallest
o - field containing a given family of sets . Proof . There is at least one field ,
namely the field of all subsets of S , which contains a given family t . The
intersection ...
There is a uniquely determined smallest field and a uniquely determined smallest
o - field containing a given family of sets . Proof . There is at least one field ,
namely the field of all subsets of S , which contains a given family t . The
intersection ...
Page 455
Let G = U_Yn ; then f is determined by G. It follows that if F is a denumerable
subset of X * , there exists a denumerable subset Gf of X * such that each f € F is
determined by GF We can even assert that each continuous linear functional |
can be ...
Let G = U_Yn ; then f is determined by G. It follows that if F is a denumerable
subset of X * , there exists a denumerable subset Gf of X * such that each f € F is
determined by GF We can even assert that each continuous linear functional |
can be ...
Page 657
... after t seconds have elapsed , have passed into a uniquely determined new
state y . Since y is uniquely determined by x and t , a function be on S to S is
defined by the equation y = $ + ( x ) . The flow is assumed to have the property
that ( i ) ...
... after t seconds have elapsed , have passed into a uniquely determined new
state y . Since y is uniquely determined by x and t , a function be on S to S is
defined by the equation y = $ + ( x ) . The flow is assumed to have the property
that ( i ) ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
87 other sections not shown
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Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |