  For a compact metric space $(K, \rho)$, the predual of $Lip(K, \rho)$ can be
identified with the normed space $M(K)$ of finite (signed) Borel measures on
$K$ equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich
[20]. Here we deduce atomic decomposition of $M(K)$ by mean of some results
from [10]. It is also known, under suitable assumption, that there is a natural
isometric isomorphism between $Lip(K, \rho)$ and $(lip(K, \rho))_{**}$ [15]. In
this work we also show that the pair $(lip(K, \rho), Lip(K, \rho))$ can be
framed in the theory of o-O type structures introduced by K. M. Perfekt.
