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ABSTRACT. Riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions. The decomposition of excessive measures is given for Borel right processes. The results for excessive functions are formulated within the framework of weak duality. These results extend and generalize the pioneering work of Hunt in this area.

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Journal of Functional Analysis 215 (2004) 399-426. doi:10.1016/j.jfa.2004.01.001Received by publisher: 2003-09-12Harvest Date: 2016-01-04 12:20:11DOI: 10.1016/j.jfa.2004.01.001Page Range: 399-42