By a projectivized measure I mean a nonzero measure on some measurable space $X$ up to scaling. If a nonzero measure is finite, its projectivization can be identified with its normalization (to have total measure $1$), hence can be thought of as a probability measure; however, if a measure is not finite, its projectivization still resembles a probability measure in several ways, e.g. in that it can be used as a prior in Bayesian inference. For a more purely mathematical application, Haar measure on both compact and noncompact groups can be thought of as a unique projectivized measure.
I googled both "projective measure" and "projectivized measure" but the former refers to not one but two other concepts and the latter barely returns any hits at all. Does anyone know if this concept has another established name?