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On an Invariant Borel Measure in Hilbert Space

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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 μ are neither equivalent nor orthogonal. This extends a result established in [7].

On Ordinary and Standard Lebesgue Measures on

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

New concepts of Lebesgue measure on are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on for α = (1,1,...).

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