Spectral measure of a stationary time series ($\gamma (k)={\int }_{-\pi }^{\pi }{e}^{ik\omega }dF(\omega )$)

The spectral measure of a weakly stationary process is the finite nonnegative measure whose Fourier coefficients are its autocovariances. Its total mass is the process variance. A time-series spectral density exists exactly when this measure is absolutely continuous with respect to Lebesgue measure.