We consider the exchange of a heterogeneous divisible commodity modeled as a measurable space. Under rational, continuous and convex preferences over characteristic measures a weak core is shown to exist. Further, a core exists if characteristic measures are mutually absolutely continuous. Applied to the land trading economy, the core existence results in Berliant (J Math Econ 14:53-56, 1985) and Dunz (Reg Sci Urban Econ 21:73-88, 1991) are obtained. © 2008 Springer-Verlag.