The class of mixtures of a one-parameter additively-closed family of distributions is proved identifiable. A condition for a class of scale parameter mixtures to be identifiable is indicated and applications to Type III and uniform distributions are made.
"Identifiability of Mixtures." Ann. Math. Statist. 32 (1) 244 - 248, March, 1961. https://doi.org/10.1214/aoms/1177705155