Equidistribution formulation of the dynamical Mordell–Lang conjecture

Let $X$ be a variety over an algebraically closed field $\mathbf{k}$, let $X_f(\mathbf{k})$ denote the points whose orbits under a dominant rational self-map $f:X\dashrightarrow X$ are well defined, and let $\eta$ be the generic point of $X$. For $x\in X_f(\mathbf{k})$, write $O_f(x)$ for its orbit and let $\delta_y$ denote the Dirac measure at $y$ in the constructible topology.

Dynamical Mordell–Lang equidistribution conjecture. If $x\in X_f(\mathbf{k})$ and $O_f(x)$ is Zariski dense in $X$, then

$$\lim_{n\to\infty}\delta_{f^n(x)}=\delta_{\eta}.$$

This is presented as an equidistribution interpretation of the dynamical Mordell–Lang conjecture, using the characterization of generic sequences in the constructible topology. The supplied text does not state whether this formulation is known or open.