Abstract
We provide an infinite dimensional version of Rademacher's theorem in a linear space provided with a bounded Radon measure μ. The underlying concepts of the Lipschitz property and differentiability hold μ-almost everywhere and only in the linear subspace of directions along which μ is quasiinvariant. The particular case where (X, μ) is the Wiener space (and for which the subspace of quasiinvariance coincides with the Cameron-Martin space) was proved in Enchev and Stroock (1993).
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Partially supported by the fund for promotion of research at the Technion.
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Bogachev, V.I., Mayer-Wolf, E. Some remarks on Rademacher's theorem in infinite dimensions. Potential Anal 5, 23–30 (1996). https://doi.org/10.1007/BF00276694
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DOI: https://doi.org/10.1007/BF00276694