I am looking for a small treatment of basic theorems about infinite products ; surprisingly enough they are nowhere to be found after googling a little. The reason for this is that I am beginning t...

6 Show that if a $\sigma$-algebra is infinite, that it contains a countably infinite collection of disjoint subsets. An immediate consequence is that the $\sigma$-algebra is uncountable.

An Infinite cyclic group has exactly two generators. Ask Question Asked 13 years, 7 months ago Modified 2 years, 1 month ago

Suppose there is a family (can be infinite) of measurable spaces. What are the usual ways to define a sigma algebra on their Cartesian product? There is one way in the context of defining product

4 You need to endow your infinite set with a measure such that the whole space has measure $1$ and then integrate (and hope that your function is measurable to begin with). For finite sets, the obvious …

Just out of curiosity, I was wondering if anybody knows any methods (other than the integral test) of proving the infinite series where the nth term is given by $\frac {1} {n^2}$ converges.

Richard Thompson's groups $T$ and $V$ are well-known examples of infinite simple groups. See this answer of mine for more details, or look up the article Introductory notes on Richard Thompson's …

If determinant is zero, then apart from trivial solution there will be infinite number of other, non-trivial, solutions.

And you shouldn't say "infinite primes" when you mean "infinitely many primes". "Infinite primes" would be primes each one of which is infinite. In colloquial speech the word "infinite" may be used that way, …

You are right to be suspicious. We usually define an infinite sum by taking the limit of the partial sums. So $$1+2+3+4+5+\dots $$ would be what we get as the limit of the partial sums $$1$$ $$1+2$$ …