Understanding some more set theory for statistics

[universalis]

Hope this is the right forum for my question.

I'm into statistics and quite often see assumptions involving set theory. I know some set theory but am having trouble understanding it for any application. I would like to narrow this gap, maybe because this type of mathematics seems most interesting to me or Maybe because it seems so hard? Anyway, my problem when studying some books is that I'm having a hard time imagining any set theory than the most basic. For example, I've looked at descrptive set theory, it seemed hard though. Therefore I would like to ask you about any book you could recommend.

My question is a bit fuzzy but I hope you know what I mean. Thanks!

 

[Stephen Tashi]

To get good advice, I think you must indicate the level of set theory you want to study.

Elementary probability theory uses concepts such as intersection, complement, union, De Morgan's laws.

It uses permutations and combinations of sets of things - Is that part of the set theory you want to study?

Advanced probability uses limits of sequences of sets, sigma algebras of sets.

It may use topological properties of sets such as "everywhere dense", "connected".

It may use properties of set cardinality such as "countably infinite".

 

[universalis]

Yes, sigma algebras, filtrations, probability spaces, etc. are some of the things I would like to read more about. For example, what is meant by a Polish space being used as a state space.