Introduzione
Abstract
En
Given a set
, a finitely additive probability measure
on
is considered. Let
be "strongly" non-atomic: we prove that there exists a sequence
of subsets of
(mutually disjoint and with
) whose union has measure equal to an arbitrarily given 𝛼 (with
) and such that
is countably additive on them. As a simple corollary, the following property (well-known for countably additive measures)is deduced: the range of
is the whole interval [0,1]. In the last part of the paper, some aspects of a decomposition theorem by B. De Finetti (for an arbitrary
) are deepened.
Given a set
![ω](http://212.189.136.205/plugins/generic/latexRender/cache/45bf03a575f6e81359314e906fb2bff3.png)
![\mu](http://212.189.136.205/plugins/generic/latexRender/cache/c9faf6ead2cd2c2187bd943488de1d0a.png)
![P(ω)](http://212.189.136.205/plugins/generic/latexRender/cache/8f70c3ca503cee0c42539ae23c2f4205.png)
![\mu](http://212.189.136.205/plugins/generic/latexRender/cache/c9faf6ead2cd2c2187bd943488de1d0a.png)
![(F<sub>n</sub>)](http://212.189.136.205/plugins/generic/latexRender/cache/6140feef353278e0faeb167026c621e8.png)
![ω](http://212.189.136.205/plugins/generic/latexRender/cache/45bf03a575f6e81359314e906fb2bff3.png)
![\mu ({F<sub>n</sub>} >0)](http://212.189.136.205/plugins/generic/latexRender/cache/b68200eab14cbb345cf748e65e0c7e78.png)
![0< 𝛼 ≤ \mu(ω)=1](http://212.189.136.205/plugins/generic/latexRender/cache/c1d4379278ab2b2c8a6dd35a247524ff.png)
![\mu](http://212.189.136.205/plugins/generic/latexRender/cache/c9faf6ead2cd2c2187bd943488de1d0a.png)
![\mu](http://212.189.136.205/plugins/generic/latexRender/cache/c9faf6ead2cd2c2187bd943488de1d0a.png)
![\mu](http://212.189.136.205/plugins/generic/latexRender/cache/c9faf6ead2cd2c2187bd943488de1d0a.png)
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