NONMEASURABLE AUTOMORPHISMS OF LIE GROUPS RELATIVE TO REAL- AND NON-ARCHIMEDEAN-VALUED MEASURES

摘要

In this paper, we study the problem on the existence of nonmeasurable automorphisms of finite-dimensional and infinite-dimensional Lie groups over the field of real numbers and also over non-Archimedean local fields. The nonmeasurability of automorphisms is considered relative to real-valued measures and also measures with values in non-Archimedean local fields. Their existence is proved and a procedure for their construction is given. Their application to the construction of nonmeasurable irreducible unitary representations is demonstrated.