报告内容简介：
I first explain a theory of conditional expectations for random variables with values in a complete metric space equipped with a contractive barycentric map b, and then give convergence theorems for martingales of b-conditional expectations. I give the Birkhoff ergodic theorem for b-values of ergodic empirical measures and provide a description of the ergodic limit function in terms of the b-conditional expectation. Moreover, the large derivation property of b-values of i.i.d. empirical measures is obtained by applying the Sanov large deviation principle.

主持人：詹兴致 教授