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Page 112
A function f on S to X is u - integrable on S if there is a sequence { In } of u -
integrable simple functions converging to f in u - measure on S and satisfying in
addition the equation lim \ m ( s ) — ( s ) [ o ( u , ds ) = 0 . m , Such a sequence of
u ...
A function f on S to X is u - integrable on S if there is a sequence { In } of u -
integrable simple functions converging to f in u - measure on S and satisfying in
addition the equation lim \ m ( s ) — ( s ) [ o ( u , ds ) = 0 . m , Such a sequence of
u ...
Page 113
A function f on S is u - integrable if and only if it is v ( u ) - integrable . If f is j -
integrable so is \ ( ö ) . If { In } is a sequence of u - integrable simple functions
determining s in accordance with the preceding definition , then the sequence { \ t
...
A function f on S is u - integrable if and only if it is v ( u ) - integrable . If f is j -
integrable so is \ ( ö ) . If { In } is a sequence of u - integrable simple functions
determining s in accordance with the preceding definition , then the sequence { \ t
...
Page 180
The u - integrability of fg follows from Theorem 2 . 22 when it is observed ( by
Theorem 4 ) that \ \ ( ö ) g ( 0 ) | is u - integrable . Theorem 4 applies in the same
manner to prove the 2 - integrability of g when it is assumed that fg is u -
integrable .
The u - integrability of fg follows from Theorem 2 . 22 when it is observed ( by
Theorem 4 ) that \ \ ( ö ) g ( 0 ) | is u - integrable . Theorem 4 applies in the same
manner to prove the 2 - integrability of g when it is assumed that fg is u -
integrable .
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Contents
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Exercises | 33 |
Copyright | |
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