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INCREASING SEQUENCES OF SUPERMARTINGALES
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a-algebra of Borel a-excessive assume Borel subsets branch points compact metric space completing the proof continuous functions convex cone COROLLARY cp(A cp(x defined definition denote evanescent excessive functions exists fact Feller process finite measure fixed follows G measurable hence homeomorphism Hunt process hypotheses implies increasing sequence indistinguishable isometry kernel Laplace transforms left limits LEMMA Let f Let g linear Lusinien Markov processes Markov property measurable process measurable space monotone class theorem nearly Borel notation original topology outer measure previsible stopping PROPOSITION proving quasi-left-continuous Ray process Ray resolvent Ray topology Ray-Knight reader Recall REMARK resp result right process Section semigroup separates the points standard process statement strong Markov sub-Markov subspace topology suffices to show supermartingale supermedian suppose surely right continuous theorem totally bounded metric trace U-space Ua(x Uaf(x uniformly continuous union of graphs universally measurable