can we get a family of classifiers $\left\{f_n\right\}_{n \in N}$such that $\lim_{n->∞} (E_{(X_1, Y_1), ...,(X_n, Y_n) \sim \rho}[R(f_n)]-R(f_B))=0 $

Question

For a given classifier $f: \mathbb{R}^d \mapsto\{0,1,2\}$, let $$ R(f):=\mathbb{E}_{(X, Y) \sim \rho}\left[\mathbb{1}_{f(X) \neq Y}\right] $$ $f_B$ the Bayes classifier.
can we get a family of classifiers $\left\{f_n\right\}_{n \in \mathbb{N}}$, where each $f_n$ depends only on a collection of training data $\left(X_1, Y_1\right) \ldots,\left(X_n, Y_n\right)$ sampled form $\rho$, and not on the distribution $\rho$ itself, such that: $$ \lim _{n \rightarrow \infty}\left(\mathbb{E}_{\left(X_1, Y_1\right), \ldots,\left(X_n, Y_n\right) \sim \rho}\left[R\left(f_n\right)\right]-R\left(f_B\right)\right)=0 $$ It would be better if there were a proof or explanation.