Hunt's hypothesis (H) and triangle property of the Green function
Let X be a locally compact abelian group with countable base and let W be a convex cone of positive numerical functions on X which is invariant under the group action and such that (X, W) is a balayage space or (equivalently, if 1 epsilon W) such that W is the set of excessive functions of a Hunt process on X, W separates points, every function in W is the supremum of its continuous minorants in W, and there exist strictly positive continuous u, v epsilon W such that u/v -> 0 at infinity. Assuming that there is a Green function G > 0 for X which locally satisfies the triangle inequality G (x, z) A G (y, z) <= CG (x, y) (true for many Levy processes), it is shown that Hunt's hypothesis (H) holds, that is, every semipolar set is polar.
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95-100
95-100
Elsevier