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Absolute Continuity of Measures

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Integration in Hilbert Space

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete ((MATHE2,volume 79))

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Abstract

Absolute continuity and singularity play a very important role in the study of measures in infinite-dimensional spaces, for example, Hubert space. Although there can be no theory treating such questions for finite-dimensional spaces which of great interest, such a theory for infinite-dimensional spaces is possible. It contains such topics as the investigation of the absolute continuity and singularity of various concrete classes of measures, the finding of general conditions for absolute continuity or singularity in terms of finite-dimensional distributions, and other characteristics defining the measures. An important problem is the calculation of the density of a measure w.r.t. another when the measures are absolutely continuous and the determination of the non-overlapping sets on which singular measures are concentrated.

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© 1974 Springer-Verlag Berlin Heidelberg

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Skorohod, A.V. (1974). Absolute Continuity of Measures. In: Integration in Hilbert Space. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65632-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-65632-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-65634-7

  • Online ISBN: 978-3-642-65632-3

  • eBook Packages: Springer Book Archive

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