Given iid samples $X_1,...,X_N$ drawn from some unknown distribution with not necessarily continuous density function $f(x)$ are there any theorems/papers where based on the data $X_1,...,X_N$ an estimator $f_N(x)$ of $f(x)$  is defined and the approximation rate 
$$\int_{\mathbb{R}}|f(x)-f_N(x)|dx$$
is estimated?