Looking for rigorous proof of the following fact

Question

Histogram converges to the density function asymptotically (i.e. $n\to\infty$ and interval length $h_n\to 0$). Any help or source will be helpful. Histogram of $f$ is the following:(the partition is like $\dots r_{-1}<r_0<r_1\dots$ and $r_i's$ are real.) $$\hat{f_n(x)}=\frac{1}{nh}\sum_{i=1}^n \mathbb{1}_{\{X_i-r_{0} \in (hk_x,h(k_x+1)]\}}$$ where $k_x=\lfloor{(x-r_0)/h}\rfloor$