Foundations of Quasi-Sure Analysis: Hierarchy of Capacities and Precise Gaussian Probability Spaces

  • Paul Malliavin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 313)


Capacities on a numerical model — Tigtness of capacities — Quasicontinuous functions — Tchebycheff inequalities — Redefinitions — Positive generalized functionals, their representation by a Borel measure — Equilibrium potentials — Continuity of capacities — Capacitability of Borel stes — Equilibrium measures — Measures of finite energy — Charge and capacity — Slim sets are null sets for all measures of finite energy — Invariance of capacities under a change of numerical model, precise Gaussian probability space — Quasi-sure analysis on an abstract Wiener space.


Borel Measure Equilibrium Potential Equilibrium Measure Finite Energy Positive Borel Measure 
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© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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