- Tytuł:
- On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets
- Autorzy:
-
Kwapień, Stanisław
Sawa, Jerzy - Powiązania:
- https://bibliotekanauki.pl/articles/1292703.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian measures of large and small balls in a Hilbert space.
- Źródło:
-
Studia Mathematica; 1993, 105, 2; 173-187
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł