On an Invariant Borel Measure in Hilbert Space

• Autorzy: G. Pantsulaia
• Języki publikacji: EN

Abstrakty

EN

An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold $𝕀_{μ}$ of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift $μ^{(a)}$ of μ by a vector $a ∈ ℓ₂∖𝕀_{μ}$ are neither equivalent nor orthogonal. This extends a result established in [7].

Kategorie tematyczne

• 60G15: Gaussian processes
• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
• 28A35: Measures and integrals in product spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 1
• Strony: 47-51

Daty

wydano

2004

Twórcy

autor

G. Pantsulaia

• Department of Mathematics, Georgian Technical University, 77 Kostava St., 0175 Tbilisi 75, Georgia

Identyfikatory

DOI

10.4064/ba52-1-5