Let be a random variable on the probability space and let be a sub- -algebra. Show that , up to an event of zero probability. Show that is actually the largest G-measurable event that contains the event , up to zero probability events.
Let be a random variable on the probability space and let be a sub- -algebra. Show that , up to an event of zero probability. Show that is actually the largest G-measurable event that contains the event , up to zero probability events.