Conditional Expectation: Generalized Properties

This lecture presents a proposition regarding conditional expectation for two random variables, where one is independent of a sub-sigma field and the other is measurable by it. The result shows how to compute the conditional expectation of a square integrable function of the variables, emphasizing the importance of independence and measurability. The properties discussed provide a clear method for evaluating conditional expectations, highlighting the significance of averaging and direct substitution in the process.