Recent content by tunaaa

Many thanks

Is it possible that 2 sigma-algebras could be independent under one measure but not independent under another? Many thanks.

This appears to be the only difference between a sigma-algebra and a Dynkin system: Sigma-algebra is closed under countable union Dynkin system is closed under countable union of disjoint sets This seems to result in the D-system not being a pi-system (while the sigma-alg is). Why...

OK fair enough, but that still doesn't explain why the rationals aren't in the algebra to begin with. I apologize for being slow to understand your argument. Thanks

Thanks - but to me that just suggests the rationals should in fact be in the algebra, rather than proving a contradiction. Why are the rationals not in the algebra to begin with?

Thanks. So could you give an example of a set that is an algebra, but not a sigma algebra? Thanks

Hello, first I’d like to clarify that the only difference between an algebra and a sigma-algebra, is that we have A,B \in \mathcal{A} \Rightarrow A \cup B \in \mathcal{A} \text{ (1) for } \mathcal{A} \text{ algebra}A_1, A_2, A_3, \ldots\in\mathcal{A} \Rightarrow \bigcup_{i=1}^{\infty}A_i...

Correction: \lim_{x \rightarrow a} f(g(x)) = f(\lim_{x \rightarrow a} g(x))

Sorry, replace n with x - was very tired!

Hello, I was just wondering if is it true that the limit of a monotonic transformation of a function is the same as the monotonic transformation of its limit? That is, does \lim_{n \rightarrow a} f(g(x)) = f(\lim_{n \rightarrow a} g(x)) for monotonic f, some a, and such that if the limit...

OK, sure - but how is that fact relevant to understanding the above equation? Thanks.

Hello, in relation to Markov chains, could you please clarify the following equations: In particular, could you please expand on why the first line is equal. Surely from , along with the first equation, this implies that: I just don't see why they are all equal. Please could you...