In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ-field and random variable that determine it. So we prove that it is continuous for the L^1 (X) convergence of the sub-σ-fields and of the random variables. We also present a sufficient condition for the L^1(X)-convergence of the sub-σ-fields. Then we extend the work to the set valued conditional expectation using the Kuratowski-Mosco (K-M) convergence and the convergence in the Δ-metric. We also prove a property of the set valued conditional expectation.