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Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability

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  • We discuss some recent developments of the theory of $BV$ functionsand sets of finite perimeter in infinite-dimensional Gaussianspaces. In this context the concepts of Hausdorff measure,approximate continuity, rectifiability have to be properlyunderstood. After recalling the known facts, we prove aSobolev-rectifiability result and we list some open problems.
    Mathematics Subject Classification: Primary: 28C20, 49Q15, 26E15; Secondary: 60H07.


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