The principal result of this paper is that HO is a logmodular algebra on the maximal ideal space of Lw(m), i.e., that each real-valued function in L(m) is the logarithm of the modulus of an invertible function in the algebra H'. This enables us to deduce from (a) and (b) the bulk of the generalized analytic function theory which is valid for logmodular algebras [ 8]. Srinivasan and Wang [ 10] have shown that this "function theory" follows if one assumes (a), (b), and (c) A + A is dense in L2(m). Lumer [9] has demonstrated the results under the assumption that A is an algebra of continuous functions on a compact Hausdorff space, m is a Borel measure on X which is multiplicative on A, and no other positive measure on X induces the same linear functional on A as does m. In ?5, we shall comment on this function algebra setting.