  Muon spin relaxation ($\mu$SR) measurements were carried out on
SrDy$_2$O$_4$, a frustrated magnet featuring short range magnetic correlations
at low temperatures. Zero-field muon spin depolarization measurements
demonstrate that fast magnetic fluctuations are present from $T=300$ K down to
20 mK. The coexistence of short range magnetic correlations and fluctuations at
$T=20$ mK indicates that SrDy$_2$O$_4$ features a spin liquid ground state.
Large longitudinal fields affect weakly the muon spin depolarization, also
suggesting the presence of fast fluctuations. For a longitudinal field of
$\mu_0H=2$ T, a non-relaxing asymmetry contribution appears below $T=6$ K,
indicating considerable slowing down of the magnetic fluctuations as
field-induced magnetically-ordered phases are approached.
