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 166
If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a field of subsets of E , and
that E ( E ) is the family of all sets AE , A € X , and that if Eis a o - field , then E ( E )
is a o - field . Σ ( Ε ) is called the restriction of Σ to E. If Σ , is a field , Εε Σ . , and ...
If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a field of subsets of E , and
that E ( E ) is the family of all sets AE , A € X , and that if Eis a o - field , then E ( E )
is a o - field . Σ ( Ε ) is called the restriction of Σ to E. If Σ , is a field , Εε Σ . , and ...
Page 201
The symbol will be used for the o - field of sets in S determined by Ey . The family
of all sets in S of the form S , XER with Ε ε Σ will be denoted by Σπ . 18 LEMMA .
For each a the family In is a field of sets in S and Ei = U241 . PROOF .
The symbol will be used for the o - field of sets in S determined by Ey . The family
of all sets in S of the form S , XER with Ε ε Σ will be denoted by Σπ . 18 LEMMA .
For each a the family In is a field of sets in S and Ei = U241 . PROOF .
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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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