Mathematical utility theory and the representability of demand by continuous homogeneous functions

The resort to utility-theoretical issues will permit us to propose a
constructive procedure for deriving a homogeneous of degree one continuous
function that gives raise to a primitive demand function under suitably mild
conditions. This constitutes the first self-contained and elementary proof of a
necessary and sufficient condition for an integrability problem to have a solution by
continuous (subjective utility) functions.