Existence of Lindahl equilibria in measure theoretic economies without ordered preferences

A proof of the existence of Lindahl equilibria is given for a class of measure theoretic economies, possibly atomless, in which consumers' preferences need be neither complete nor transitive. This is done as an application of a nonstandard-analytic technique that allows for the derivation of statements concerning measure theoretic economies from analogous finite economy propositions. This approach to the problem allows use of Foley's method of working with an associated private goods economy without the dimension of the commodity space in the associated economy becoming problematic. Potential extensions of the technique used are also discussed.