D. Mauldin presented
conditions under which the dual of ca(S,Σ) could be given an integral representation.
W. D. L Appling gave a “pseudo-representation” for the dual of ba(S,Σ), but the
latter was not the type obtained by Mauldin. This paper gives conditions that are
necessary and sufficient for the existence of the classical type integral representation
for the dual of ba(S,Σ).