# Continuous selection parameterizing discrete measures

Let $$\mathcal{P}_n(\mathbb{R})$$ denote the set of probability measures on $$\mathbb{R}$$ for the form $$\sum_{i=1}^n k_i \delta_{x_i}$$. Then any measure in $$\mathcal{P}_n(\mathbb{R})$$ is in the image of the map on $$\Delta_n \times \mathbb{R}^n$$, where $$\Delta_n$$ is the $$n$$-simplex, taking $$(k_1,\dots,k_n)\times (x_1,\dots,x_n)$$ to $$\sum_{i=1}^n k_j \delta_{x_i}$$. Clearly this map is continuous, when $$\mathcal{P}_n(\mathbb{R})$$ is equipped with the Prokhorov metric.

However, is it clear that it admits a continuous selection? Ie.: a continuous right inverse (definitely not unique of course)?
