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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

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The field of crystal structure prediction (CSP) has changed dramatically over the past decade and methods now exist that will strongly influence the way that new materials are discovered, in areas such as pharmaceutical materials and the discovery of new, functional molecular materials with targeted properties. Machine learning (ML) methods, which are being applied in many areas of chemistry, are starting to be explored for CSP. This article discusses the areas where ML is expected to have the greatest impact on CSP and its applications: improving the evaluation of energies; analyzing the landscapes of predicted structures and for the identification of promising molecules for a target property. Graphical abstract