# The distribution approach to spatial economics.

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## Abstract

JOURNAL OF REGIONAL SCIENCE, VOL. 24, NO. I , 1984 THE DISTRIBUTION APPROACH TO SPATIAL ECONOMICS Thijs ten Raa* 1. INTRODUCTION This article exposes a new approach to spatial economics which is general yet operational. This idea is straightforward. The approach is essentially a modifica- tion, or more precisely a spatialization, applicable to any standard, nonspatial model. Standard models are usually comprised of structures and of activities, formally represented by elements of real vector spaces, such as scalars, vectors, or matrices. Basically, the structures and activities will now be represented by spatial distributions of those elements. In other words, the scalars, vectors, and matrices are spread out over geographical space. Formally, the real vector spaces are replaced by vector-valued distribution spaces. So far the notion of spatialization will not have excited the revolutionary zeal of the theorist for (s)he is already acquainted with studies in which structures and activities have spatial components. Moreover, such refinements merely seem to increase computational complexity without affecting the mechanics of the model at hand. It is at this junction that our approach deviates and is truly new. We shall not chop up structures and activities in spatial bits and then proceed as usual. Instead we will consider spatialized structures and activities as single elements in a distribution space. The novelty is that the manipulations will apply directly to the spatialized structures and activities, as if they are ordinary numbers, vectors, or matrices. For this purpose we shall draw on the theory of distributions developed in 1945 by Schwartz (1957). Economists who want to make creative use of the present article must definitely read Schwartz’ (1961) introduction to the theory, since in the present work the mathematics chapter “Theory of Distributions” is applied for the first time in economic science. Our distribution approach to spatial economi

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