  For every frame spectral measure $ \mu $, there exists a discrete measure $
\nu $ as a frame measure. Since if $ \mu $ is not a frame spectral measure,
then there is not any general statement about the existence of frame measures $
\nu $ for $ \mu $, we were motivated to examine Bessel and frame measures. We
construct infinitely many measures $ \mu $ which admit frame measures $ \nu $,
and we show that there exist infinitely many frame spectral measures $ \mu $
such that besides having a discrete frame measure, they admit continuous frame
measures too.
