[944] Measurability of a RV

[Richard Rosenbaum]

Say G is a sigma algebra and F is a smaller sigma algebra contained in G.

Say X is a RV that is G-measurable.

Why is X not also F-measurable?

This idea was discussed briefly in the TA session on Friday, but I am still
a bit confused. My intuition would be that since G is larger, and X is
measurable with respect to G, then X would also be measurable with respect
to F since it is contained in G.

If anyone could share their thoughts, it would be much appreciated.


Regards,
Rich

-- 
Richard Rosenbaum
Master of Science in Computational Finance Candidate
Carnegie Mellon University - Class of Dec. 2018
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