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m.a.
  • Member for 11 years
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 Student
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Recovering measure from the family of sigma-subalgebras
@EmilJeřábek thanks, you've finally ruined my conception of the subject.
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revised
Recovering measure from the family of sigma-subalgebras
changed the condition of consistency, thanks to Emil Jeřábek
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Recovering measure from the family of sigma-subalgebras
@EmilJeřábek thanks, it seems I have to demand of $\mu_\alpha(A) \le \mu_\beta(B)$ when $A\subseteq B$.
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Recovering measure from the family of sigma-subalgebras
@MonroeEskew Thanks for a good counterexample. Well, as far as I can see, I have to ask another question: is it possible to continue the measure to $\sigma (\mathscr{F}_{\alpha}, \alpha \in \mathfrak{A})$?
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Recovering measure from the family of sigma-subalgebras
@GarlefWegart Well, it might be not as simple as it seems. To begin with, in some sence it's a generalization of Kolmogorov theorem. Also, as I can see, your property of compatibility is too strong and I'm not sure I want to use it.
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Recovering measure from the family of sigma-subalgebras