On an Invariant Borel Measure in Hilbert Space
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 47-51
MSC: 28A35, 28C20, 60G15.
DOI: 10.4064/ba52-1-5
Abstract
An example of a nonzero -finite Borel measure \mu with everywhere dense linear manifold {{\Bbb I}}_{\mu } of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space \ell _2 such that \mu and any shift \mu ^{(a)} of \mu by a vector a \in \ell _2 \setminus {{\Bbb I}}_{\mu } are neither equivalent nor orthogonal. This extends a result established in [7].
