Muon spin relaxation and magnetic susceptibility measurements have been performed on the pure and diluted spin 1/2 kagomé system (CuxZn(1-x))3V2O7(OH)2 2H2O. In the pure x=1 system we found a slowing down of Cu spin fluctuations with decreasing temperature towards T approximately 1 K, followed by slow and nearly temperature-independent spin fluctuations persisting down to T=50 mK, indicative of quantum fluctuations. No indication of static spin freezing was detected in either of the pure (x=1.0) or diluted samples. The observed magnitude of fluctuating fields indicates that the slow spin fluctuations represent an intrinsic property of kagomé network rather than impurity spins.