Automorphism groups of measurable spaces (Q1109910)

The purpose of this paper is to find the possible automorphism groups for rigid separable measurable spaces. The authors show that there is only one such non-trivial group which is Abelian (a countable product of two element groups) and that this group is realized as the automorphism group of some separable space. A particular class of such spaces is characterized in terms of rigid components. Finally, an example of a measurable space which is rigid in the strict sense is constructed.