Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a 1-periodic function. I am looking about the conditions on $(a,b)\in\mathbb{R}^2$ such that we have the property : $$\frac{1}{n}\sum_{\ell=0}^{n-1}f(a+b\ell)\underset{n\rightarrow +\infty}{\longrightarrow}\int_0^1 f(x)dx.$$ Thank you for your help !