## The prior distribution of a random measure

### Volume 46 / 2019

#### Abstract

It is known that an infinite, exchangeable sequence of observations from a Borel space, in particular a Polish one, is underlain by an almost surely (a.s.) unique random probability measure on this space such that, conditioned on it, the observations are independent and identically distributed with that measure. The distribution of that random measure is the prior distribution involved in Bayes inference. The present paper proves that the prior distribution of the a.s. unique random measure underlying an infinite, exchangeable sequence of observations from a Polish space is a Radon probability measure on the $\sigma $-field generated by the narrow topology in the space of Borel probability measures on the starting Polish space.