This article is cited in 3 papers

Measurability of representations of locally compact groups

S. V. Lyudkovskii

General Physics Institute named after A. M. Prokhorov, Russian Academy of Sciences

Abstract: It is shown that a locally compact group is discrete if and only if all its irreducible unitary representations are weakly Haar-measurable. Furthermore, it is proved that an Abelian locally compact group is discrete if and only if all its characters are measurable. Similar results are obtained for complete Abelian groups and generalized loop groups.

UDC: 512

MSC: Primary 22D10; Secondary 22F65, 20E18

Received: 02.07.1993

 English version: Sbornik: Mathematics, 1995, 186:2, 245–255

Bibliographic databases:

• 
• 
•