Assume you are given a probability space $ ( \Omega, \mathcal{ F}, P ) $, a bounded random variable $ X $ on $ ( \Omega, \mathcal{ F}, P) $, and a sub-$\sigma$-algebra $ \mathcal{A} $ of $ \mathcal{F} $.
Is it true that the conditional expectation $ E[X | \mathcal{A}] $ of $ X $ given $ \mathcal{A} $ is again a bounded random variable?
Thanks a lot for your help! Regards, Si