%0 Journal Article
%@ 0167-7152
%A Crimaldi, Irene
%A Pratelli, Luca
%D 2005
%F eprints:987
%I Elsevier
%J Statistics and probability letters 
%K Conditional expectation; Convergence in distribution; Convergence in total variation
%N 2
%P 151-162
%T Two inequalities for conditional expectations and convergence results for filters
%U http://eprints.imtlucca.it/987/
%V 74
%X In this paper we prove, first of all, two inequalities for conditional expectations, from which we easily deduce a result by Landers and Rogge. Then we prove convergence results for conditional expectations of the form Pn [f(Xn)|Yn] to a conditional expectation of the form P [f(X)|Y]. We study, in particular, the case in which the random variables Yn  Y are of the type hn (Xn), h(X)