Linear Operators, Part 1 |
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Page 182
Thus da / dụ is defined u - almost everywhere by the formula ( da 2 ( E ) = u ( ds )
, Εε Σ . We close this section with a generalization of many " change of variable ”
theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If !
Thus da / dụ is defined u - almost everywhere by the formula ( da 2 ( E ) = u ( ds )
, Εε Σ . We close this section with a generalization of many " change of variable ”
theorems . 8 LEMMA . Let S , and S , be sets and $ a mapping of S , into Sz . If !
Page 240
It is evident that if we define the set function u on { by placing ( E ) = 0 if E $ and (
$ ) = 0 , then a bounded function is E ... The space B ( S ) is defined for an
arbitrary set S and consists of all bounded scalar functions on S. The norm is
given by ...
It is evident that if we define the set function u on { by placing ( E ) = 0 if E $ and (
$ ) = 0 , then a bounded function is E ... The space B ( S ) is defined for an
arbitrary set S and consists of all bounded scalar functions on S. The norm is
given by ...
Page 516
38 ( Markov ) Let S be a non - void set and $ a function on S to S. A function u
defined on the family of subsets of S is said to be 6 - invariant in case u ( E ) = u (
0-1E ) , ECS , where 6-1E = [ sos e E. Show that there is a non - negative
bounded ...
38 ( Markov ) Let S be a non - void set and $ a function on S to S. A function u
defined on the family of subsets of S is said to be 6 - invariant in case u ( E ) = u (
0-1E ) , ECS , where 6-1E = [ sos e E. Show that there is a non - negative
bounded ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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