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Minimum representing measures in Idempotent Analysis

Cormac Walsh
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Abstract

We show that the set of max-plus measures representing a given max-plus harmonic vector has a least element. This may be viewed as an analogue of the uniqueness of the integral representation of harmonic functions in Potential Theory. As an application, we show how the distance-like functions of a metric space can be expressed in terms of the Busemann points of the metric boundary.

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Cormac Walsh. 2005-03-30. Minimum representing measures in Idempotent Analysis. https://arxiv.org/abs/math/0503716

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