According to Bochner's theorem, the covariance function $b(t)$ of a centered, weakly stationary process $X(t)_{t\geq 0}$ can be written as
$$b(t) = \int_{-\infty}^{\infty} e^{i t \lambda} \mu(d\lambda),$$
where $\mu$ is the spectral measure of the process.
Which properties of $X(t)$ are sufficient for $\mu$ being absolutely continuous w.r.t. to the Lebesgue measure?