Re: I cannot understand the sentence in a probability book.
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 2 Jan 2008 18:35:11 -0500
In article <7e8838d5-7c39-47a1-a960-a5d972b158ad@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
danheyman@xxxxxxxxx <danheyman@xxxxxxxxx> wrote:
On Jan 2, 9:34 am, water <waterloo2...@xxxxxxxxx> wrote:
When =D9 is uncountable (e.g., =D9 =3D R or [0, 1]),
it is not possible to define a reasonable measure for every subset of
=D9; for
example, it is not possible to find a measure on all subsets of R and
still
satisfy property m([a, b]) =3D b - a. This is why it is necessary to
introduce =F3-fields that
are smaller than the power set.
what is the meaning of the sentence?
Thanks
Those sentences are perfectly clear to me. What exactly don't you
understand?
This is the case if one asks for a countably additive
measure. There are, under the usual axioms for set
theory including enough of choice, finitely additive
measures with this property. But finitely additivity
are not useful in statistical problems for many reasons.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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