Mathematics Asked by Marcelo RM on November 6, 2021
I was reading the lecture notes about probability and random processes, Lecture Notes, then I’m stucked here:
Example 1.3.6 Let $Omega = mathbb R$ and suppose that we have a sigma field A such that all intervals of the form:
$[ 1, 2 – 1/n) in mathcal{A}$
So, I would like to know how to prove that interval is a $sigma$ algebra?
I know from the lecture note that:
$[1, 2) in mathcal{A}$, since $lim_{ntoinfty} [1, 2 – 1/n)$
I think its prove statement 3. Am I right?
But I don’t know how to prove statements 1 and 2.
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