scratch my above post with an important typo. use this version.


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送交者: minimax 于 2007-09-12, 21:22:59:

回答: then use counting measure if that would quench your curiosity. 由 minimax 于 2007-09-12, 21:19:29:

It is defined as follows. Let Omega be a set
of real numbers, F= {all subsets of Omega}, let mu(A)= # of integers in A for any A in F, then
mu is a measure on (Omega,F) and mu is ``counting measure''.

Counting measure is a sigma-finite measure in the sense that there exists a countable partition of Omega,
Omega=\sum_{n=1}^{\infty} A_n, A_n in F such that \mu(A_n)<\infty for any n.

so if you let Omega be your R (real line), and note R= Union (i,i+1] for i = +/- 1, +/- 2 , ....

you will get your dream fulfilled!




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