On an Invariant Borel Measure in Hilbert Space
G. Pantsulaia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004), p. 47-51 / Harvested from The Polish Digital Mathematics Library
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An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold 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∖μ are neither equivalent nor orthogonal. This extends a result established in [7].

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:280425 
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G. Pantsulaia. On an Invariant Borel Measure in Hilbert Space. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 47-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-5/