X is a random variable so is |X|?

BoogieE
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Howdy guys. Given that X is a random variable how would you prove |X| to be one too? Thanks for any suggestions!
 
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What is your definition of random variable?
 
Just mapping from (S,F) to (R, B(R))
 
X is measurable, | | is continuous hence measurable. And the composition of measurables is measurable.
 
I am expecting that from the fact that X(-1)(G) = {w in S such that X(w) is in G for all G in B(R) } is in F you can somehow show that |X|(-1)(G') = {w in S such that |X|(w) is in G' for all G' in B(R)} is also if F
 
micromass said:
X is measurable, | | is continuous hence measurable. And the composition of measurables is measurable.
I asked my math professor and she said this is ok. I probably overthought the problem. Thank you very much!
 

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