Rich Probability Space

In the setting of Probability Measures on Euclidean Space and Random Vectors: Standing Notation, the probability space $(\Omega,\mathcal{F},P)$ is called rich(i) if for every $m\in\mathbb{N}$ with $1\le m$ and every $\mu\in\mathcal{P}(\mathbb{R}^{m})$ there is a random vector $X$ in $\mathbb{R}^{m}$ on $(\Omega,\mathcal{F},P)$ whose law is $\mu$.