Abstract
In this section we shall develop some of the basic potential theory of the cone of excessive measures. We shall then prove a preliminary version of an important integral representation theorem of Fitzsimmons [F88b]. Additional properties of the cone Exc will appear as corollaries to this integral representation. The definitive form of Fitzsimmons’ theorem appears in (7.10). Its statement requires the use of Kuznetsov measures to be developed in §6. Theorems 5.9 and 5.11 below are more or less well-known. The analogous results for excessive functions may be found in [DM, XII], for example. However, proofs of the results we need are somewhat scattered in the literature and so we shall give a systematic development. Our development follows [F88b].
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© 1990 Birkhäuser Boston
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Getoor, R.K. (1990). Potential Theory of Excessive Measures. In: Excessive Measures. Probability and Its Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3470-8_5
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DOI: https://doi.org/10.1007/978-1-4612-3470-8_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8036-1
Online ISBN: 978-1-4612-3470-8
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