On the role of the Ky Fan metric in rough ideal convergence in probability

Tamim Aziz, Sanjoy Ghosal

Given a probability space $(S,\hat{I}”,\mathbb{P})$ and a separable metric space $(U,d)$, the $KyFan$ metric $\ddot{I}(X,Y)$ on the space ${\mathfrak{X}}^0$ of equivalence classes of random va…