On an Invariant Borel Measure in Hilbert Space
G. Pantsulaia (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift of μ by a vector are neither equivalent nor orthogonal. This extends a result established in [7].