(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a question about mathematical probability, using the sigma-algebra, measure and probability space approach.

Define A(t) = {all outcomes, w, in the sample space such that Y(w) < or = t}

where Y is a random variable and t is any real number.

Fix a real number X.

Consider an increasing sequence {Xn} such that Xn tend to X from below/left as n tend to infinity. Therefore, Xn < or = X for all n.

So, A(Xn) is a subset of A(X) for all n.

2. Relevant equations

N.A.

3. The attempt at a solution

This isn't a homework question but I thought it fits in this forum. It is stated in my text that the infinite union of A(Xn) is not A(X).

I think this is because Xn can tend to X in such a way that X is not equal to X all for n. So their infinite union will always not contain some element in X.

But how do I show this mathematically? A little nudge in the right direction so I can solve this myself? Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Probability - Infinite Union of Subsets of a Sample Space

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**