I will continue Jonatan Gutman's talk. It will concern further developments on the probabilistic Takens embedding theorem. I will present the following result: let $X \subset \mathbb{R}^N$ be a compact set, $\mu$ a Borel probability measure on $X$ and $T:X \to X$ a Lipschitz and injective map. Fix $k \in \mathbb{N}$ greater than the upper packing dimension of $\mu$ and assume that sets of periodic points have dimensions small enough. We prove that for a typical polynomial perturbation $\tilde{h}$ of a given Lipschitz map $h : X \to \mathbb{R}$, the corresponding $k$-delay coordinate map $\phi : X \to \mathbb{R}^k$ has the following property: for almost every $x \in X$, measure $\mu$ restricted to $\{ y \in X : |\phi(x) - \phi(y)| < \epsilon \}$ (and normalized to a probability measure) converges to the point mass in $x$ as $\epsilon$ goes to zero. This proves the conjecture of Ott, Sauer, Shroer and Yorke for exact dimensional measures. Joint work in progress with Krzysztof Barański and Jonatan Gutman.