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Gaussian Measure of the Intersection of Two Absolutely Convex Sets

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Stochastic Analysis and Related Topics VIII

Part of the book series: Progress in Probability ((PRPR,volume 53))

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Abstract

Let (W, H, µ) be a finite dimensional Wiener space and let A, B be two measurable, convex, symmetric subsets of W such that for \(A \subset {{T}^{{ - 1}}}\left( A \right)\) any contraction T. Then one has \(\mu \left( {A \cap B} \right)\mu \left( A \right)\mu \left( B \right)\).

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References

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Üstünel, A.S. (2003). Gaussian Measure of the Intersection of Two Absolutely Convex Sets. In: Çapar, U., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VIII. Progress in Probability, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8020-6_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8020-6_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9406-7

  • Online ISBN: 978-3-0348-8020-6

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