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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)

Abstract

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.

Keywords

Borel Measure Equilibrium Potential Equilibrium Measure Finite Energy Positive Borel Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Paul Malliavin

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