Existence of Random Measures Consistency Conditions for a Prospective Family

A random measure is a probability measure on a measurable space that is itself a random element of another probability space. In other words, a random measure is a probability distribution on the space of all measures on a given measurable space. In this paper, we show that mild consistency conditions on a prospective family of fidis suffice to guarantee the existence of a random measure having those fidis. The existence of classical random measures is supported by the Hausdorff measure. Random measures are defined most often as mappings from an interval onto a probability space, although they can also be defined as functions over certain spaces or as generalized densities of measurable sets. The probability measure on the first set is called a condition for this family of families.