In the standard model of electroweak interactions the positrons from the decay of polarized positive muons are mainly longitudinally polarized. The measurement of the two transverse polarization components PT1 and PT2 is a sensitive tool to look for contributions from additional, exotic interactions. The energy dependence of PT1 yields the low energy Michel parameter eta and thus an improved model-independent value of the Fermi coupling constant. A non-zero value PT2 would be the first observation of time reversal violation in a purely leptonic decay. The muon decay experiment at the Paul Scherrer Institut is the first experiment to measure all three positron polarization components, PT1, PT2, and the longitudinal polarization component PL. In this contribution results from a small data-sample taken in 1999 are presented. The values obtained are PT1 = (5 +- 16)*10^(-3), PT2 = (1 +- 16)*10^(-3), and PL = 1.09 +- 0.15. More than ten times more data was taken in October/November 2000, the analysis of which will further reduce the statistical errors.