Abstract
The concepts of polar sets and capacity are fully developed in this chapter and will culminate in the characterization of polar sets as sets of capacity zero. An essential part of this development is Choquet’s theory of capacities which has important applications to stochastic processes as well as potential theory. These concepts are used to settle questions pertaining to equilibrium distribution of charges, the existence of Green function for regions in \(R^n\), and the boundary behavior of Green functions. It will be shown that an open subset of \(R^2\) has a Green function if and only if the region supports a positive superharmonic function.
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Helms, L.L. (2014). Negligible Sets. In: Potential Theory. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-6422-7_5
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DOI: https://doi.org/10.1007/978-1-4471-6422-7_5
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