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Hauptgegenstand des Buches ist die translationsinvariante Potentialtheorie unendlich-dimensionaler lokalkompakter abelscher Gruppen. Die Darstellung ist in sich abgeschlossen und setzt nur elementare Kenntnisse aus der Funktionsanalysis und über Markov-Prozesse voraus. This is a graduate-level introduction to potential theory on infinite-dimensional locally compact abelian groups. Classical potential theory and its probabilistic counterpart is extended to the infinite-dimensional potential theory of elliptic and parabolic differential operators. Elementary knowledge of functional analysis and Markov processes is required.§