Let be a random variable. Let . Show that is measurable as a function from . Here is the Borel -algebra on . Is it sufficient just to say that for every , so is measurable from by definition?
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It's sufficient. Maybe the most interesting part of this exercise is to show that is a -algebra.
Thank you. I guess is a follows from that commutes with complements, countable intersections and unions.
Originally Posted by TheProphet I guess is a follows from that commutes with complements, countable intersections and unions. Yes.
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