Symmetric Distributions of Random Measures in Higher Dimensions

An infinite sequence of random variables X=(X ₁, X ₂,...) is said to be spreadable if all subsequences of X have the same distribution. Ryll-Nardzewski showed that X is spreadable iff it is exchangeable. This result has been generalized to various discrete parameter and higher dimensional settings. In this paper we show that a random measure on the tetrahedral space is spreadable, iff it can be extended to an exchangeable random measure on . The result is a continuous parameter version of a theorem by Kallenberg.