@article{eprints987,
          number = {2},
           pages = {151--162},
          volume = {74},
            year = {2005},
           title = {Two inequalities for conditional expectations and convergence results for filters},
          author = {Irene Crimaldi and Luca Pratelli},
       publisher = {Elsevier},
         journal = {Statistics and probability letters },
        keywords = {Conditional expectation; Convergence in distribution; Convergence in total variation},
        abstract = {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){\ensuremath{|}}Yn] to a conditional expectation of the form P [f(X){\ensuremath{|}}Y]. We study, in particular, the case in which the random variables Yn  Y are of the type hn (Xn), h(X)},
             url = {http://eprints.imtlucca.it/987/}
}