Measurable Spaces, Measure Spaces, and Measurable Functions
April 26, 2010  Posted by John Armstrong  Analysis, Measure Theory
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is it enough [tex] mathcal{S} [/tex] be a [tex] \sigma ring [/tex] a probability book i’m studying says the space needs a [tex] \sigma – Field[/tex]
Could you clarify please
thanks
Comment by cappa  April 27, 2010 
A field is a different name for a algebra. As I point out above, in many cases actually is a algebra (or field). In this case, itself is in , and so it’s clear that every point in is in some measurable set.
However, we’re going to allow to just be a ring — itself might not be in — so long as every point in is still in some measurable set.
Comment by John Armstrong  April 27, 2010 
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Is every measurable space is topological space
Comment by M. A. Hossain  September 27, 2011 
Not in any natural way. The obvious thing would be to try to use the algebra of measurable sets as the collection of open sets in the topology, but it’s not necessarily closed under arbitrary unions.
Comment by John Armstrong  September 27, 2011 
Actually my query is as follows:
If T is a sigmaalgebra In X, is T also a topology in X?
Comment by M. A. Hossain  September 28, 2011 
No, as I said; is not necessarily closed under arbitrary (uncountable) unions.
Comment by John Armstrong  September 28, 2011 