The concept of the population-density function, which is usually applied within the context of an urban area, is extended to the scale of a metropolitan-area-based region or city region. A form for such a regional density function is proposed, and this is examined for selected regions of the UK and North America. It is demonstrated how such a region-wide density function may be related to other density functions which have been used to characterise the structures of the metropolitan and non-metropolitan parts of the region. Consideration is also given to problems associated with constructing and interpreting the regional density function and to its underlying theoretical basis. Finally, the application of the density-function approach in the analysis of regional structure is briefly discussed.
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