# Exchangeable Probability Distribution

Let be a measurable space. A probability distribution on the measurable space of sequences of length , where , is exchangeable if

for any measurable and any permutation of the set (i.e., if the distribution of the sequence is invariant under any permutation of the indices).

A probability distribution on the power measurable space is exchangeable if the marginal distribution of on (defined by

for all events ) is exchangeable for each (i.e., if the distribution of the sequence is invariant under any permutation of the finite number of the indices).