Existence of a continuous utility function with path monotonicity: the Wold approach

Summary This paper uses the approach of Wold to prove the existence of a continuous utility function on a subset ofR ⁿ with a path monotonicity assumption. This result is then extended to a Banach space.The research for this paper was begun while visiting the University of Cambridge and the London School of Economics in 1988. I should like to thank Dr. A. Beardon, Professor M. Desai, Professor L. Foldes and Dr. A. Horsley for their hospitality. Also, I am grateful to an anonymous referee for comments that led to an improvement in the exposition.