  In the setting of $\R^d$ with an $n-$dimensional measure $\mu,$ we give
several characterizations of Lipschitz spaces in terms of mean oscillations
involving $\mu.$ We also show that Lipschitz spaces are preserved by those
Calderon-Zygmund operators $T$ associated to the measure $\mu$ for which T(1)
is the Lipschitz class $0.$
