Symmetry and measurability.

In the Hewitt-Savage 0-1 law, symmetric measurable sets are considered in a countable product of a σ-algebra Σ with itself. Therefore, it may be of interest to find simple generators for these sets in terms of the generators of Σ. We put the problem into a more general framework of action groups and as an application find simple generators for the finite product case. We also have a partial result in the countable product case. [ABSTRACT FROM AUTHOR]