I am studying a paper [1] which states that, as far as I understand, the probability of a single sample $x$ taken from a random variable $X$ with Gaussian distribution equals the Gaussian distribution density function
$$ \Pr(X=x) = \dfrac{1}{\sqrt{2\pi\sigma^2}}\exp\left\{-\dfrac{(x-\mu)^2}{2\sigma^2}\right\}$$
where $X \sim \mathcal{N}(\mu,\sigma^2)$.
(If you think my formulation is incorrect or imprecise, feel free to correct me and please have a look to Equation 1 of Section 3.1 in [1].)
If I remember correctly my math classes, the probability of a certain sample in a continuous probability distribution approaches zero, because probability (at least for ranges of X) is defined as the integral over the density function.
Is the approximation used in the referenced paper valid? What are the constraints, if there are some?
Addon: In this paper, they do the same for the probability of a sample in an exponential probability distribution (see Equation 2 of Section 3.2 in [1]).