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# Mathematical Research Letters

## Volume 19 (2012)

### Number 3

### The conjugacy relation on unitary representations

Pages: 525 – 535

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n3.a2

#### Authors

#### Abstract

In a 1965 paper, E.G. Effros asked the question if the conjugacy relation for unitary representations of a locally compact second countable group is a Borel equivalence relation. In this paper, we answer this question affirmatively. This also settles a recent question raised by A.S. Kechris regarding the hierarchy complexity of unitary equivalence of probability measure preserving actions of countable discrete groups.

#### 2010 Mathematics Subject Classification

03E15, 03E75, 22D10, 22D25, 46Lxx