Hi!
I am totally new to measure theory, so bear in mind that all concepts like and are new for me.
Problem:
Suppose is an algebra of subsets on and and are two contents on such that and . Prove that .
I´m not sure how to start.
Hi!
I am totally new to measure theory, so bear in mind that all concepts like and are new for me.
Problem:
Suppose is an algebra of subsets on and and are two contents on such that and . Prove that .
I´m not sure how to start.
Well if you mean by contents concentration or measure, then I think it's easy.
Assume , this is for every B in the algebra A of X, A must include X as a subset if it's a sigma algebra (because this is an algebra which is closed to finite intersection of subsets of X, and also countable union if I remember correcly), which is a contradiction to the fact that .