 Somewhat more abstractly, define the "exchangeable sigma algebra" or "sigma algebra of symmetric events" formula_3 to be the set of events (depending on the sequence of variables formula_1) which are invariant under permutations of the indices in the sequence formula_1.Then formula_6.Since any finite permutation can be written as a product of transpositions, if we wish to check whether or not an event formula_7 is symmetric (lies in formula_3), it is enough to check if its occurrence is unchanged by an arbitrary transposition formula_9, formula_10.