On an Invariant Borel Measure in Hilbert Space

G. Pantsulaia. "On an Invariant Borel Measure in Hilbert Space." Bulletin of the Polish Academy of Sciences. Mathematics 52.1 (2004): 47-51. <http://eudml.org/doc/280425>.

@article{G2004,
abstract = {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].},
author = {G. Pantsulaia},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {admissible translation; Gaussian measure; quasi invariance; invariance},
language = {eng},
number = {1},
pages = {47-51},
title = {On an Invariant Borel Measure in Hilbert Space},
url = {http://eudml.org/doc/280425},
volume = {52},
year = {2004},
}

TY - JOUR
AU - G. Pantsulaia
TI - On an Invariant Borel Measure in Hilbert Space
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 1
SP - 47
EP - 51
AB - 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].
LA - eng
KW - admissible translation; Gaussian measure; quasi invariance; invariance
UR - http://eudml.org/doc/280425
ER -