Let's say I have a point $a \in \mathcal{U}$, where $\mathcal{U}$ is a set, and $x$ is a Gaussian random variable with mean $0$ and variance $\sigma^2$. Is it mathematically correct to say:
Restrict $\sigma^2$ sufficiently small such that $a + x \in \mathcal{U}$ (or, probability of $a + x \not\in \mathcal{U}$ is 0); $a + x$ always stay in $\mathcal{U}$.
Thank you.