A Measure-Theoretic Approach to Urban Fields with Applications to Origin-Constrained Travel

Mathematical formulations of urban structure usually invoke either a strictly continuous or a strictly discrete account of spatial distributions. The arbitrary nature of this dichotomy is illustrated by urban retail and commercial activity, which can be usefully represented as a mixture of discrete and continuous components. This paper exploits concepts from general measure theory to extend the notion of an urban field. The resulting formulation yields discrete and continuous models as special cases. The abstract-field model is interpreted for the case of urban commercial structure, and is applied to develop a generalized extension of the origin-constrained interaction model. The descriptive utility of the formulation is then demonstrated in the case of commercial arterials in Albany, New York.