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Extremal properties of half-spaces for spherically invariant measures. (English) Zbl 0395.28007

MSC:
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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[1] J. Tippe, ?Zur isoperimetrischen Eigenschaft der Kugel in Riemannischen Räumen konstanter positiver Krümmung,? Math. Ann.,152, No. 2, 120?148 (1963). · Zbl 0131.20204 · doi:10.1007/BF01344002
[2] E. Schmidt, ?Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionzahl,? Math. Z.,49, 1?109 (1943). · Zbl 0028.31303 · doi:10.1007/BF01174192
[3] V. N. Sudakov, ?Geometric problems in the theory of infinite-dimensional probability distributions.? Thesis, Leningrad State University (1972).
[4] X. Fernique, ?Integrabilite des vecteurs gaussiens,? C. R. Acad. Sci., Paris,270, 1698?1699 (1970).
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