In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes in metric measure spaces. We show that if ∞ is accessible from an open set D, then there is only one Martin boundary point of D associated with it, and this point is minimal. We also prove the analogous result for finite boundary points. As a consequence, we show that minimal thinness of a set is a local property.
- Martin boundary
- Martin kernel
- Minimal thinness
- Purely discontinuous Feller process
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