Let
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si100.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=c1b8a540867c0c0ff0a9b158e1630798" title="Click to view the MathML source">Xclass="mathContainer hidden">class="mathCode"> be a locally compact abelian group with countable base and let
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si10.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=b8ad77a8cede94a7285142c3091b90f1" title="Click to view the MathML source">Wclass="mathContainer hidden">class="mathCode"> be a convex cone of positive numerical functions on
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si100.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=c1b8a540867c0c0ff0a9b158e1630798" title="Click to view the MathML source">Xclass="mathContainer hidden">class="mathCode"> which is invariant under
the group action and such that
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si4.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=ccfe2a62912a8cfc141bd9750a573a60" title="Click to view the MathML source">(X,W)class="mathContainer hidden">class="mathCode"> is a balayage space or (equivalently, if
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si318.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=8685e308bf95feb1261a46b43686a904" title="Click to view the MathML source">1∈Wclass="mathContainer hidden">class="mathCode">) such that
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the set of excessive functions of a Hunt process on
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class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si10.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=b8ad77a8cede94a7285142c3091b90f1" title="Click to view the MathML source">Wclass="mathContainer hidden">class="mathCode"> separates points, every function in
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the supremum of its continuous minorants in
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there exist strictly positive continuous
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class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si12.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=7b0e4689a6d871995eee5122c1315168" title="Click to view the MathML source">u/v→0class="mathContainer hidden">class="mathCode"> at infinity.
Assuming that there is a Green function class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si13.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=cde4c28c77e98506335514e59027bcc6" title="Click to view the MathML source">G>0class="mathContainer hidden">class="mathCode"> for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si100.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=c1b8a540867c0c0ff0a9b158e1630798" title="Click to view the MathML source">Xclass="mathContainer hidden">class="mathCode"> which locally satisfies the triangle inequality class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0723086914000784&_mathId=si15.gif&_user=111111111&_pii=S0723086914000784&_rdoc=1&_issn=07230869&md5=9f7765ded9859de8f889b717487ddbaf" title="Click to view the MathML source">G(x,z)∧G(y,z)≤CG(x,y)class="mathContainer hidden">class="mathCode"> (true for many Lévy processes), it is shown that Hunt’s hypothesis (H) holds, that is, every semipolar set is polar.