Geodesic
The uniqueness of Haar measure and set theory
Colloquium Mathematicum, Tome 74 (1997) no. 1, pp. 109-121 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits of all points of X are uncountable. In particular, this is true if either G is a locally compact, σ-compact topological group acting continuously on X, or the space X is uniform and nonseparable, and G consists of uniformly equicontinuous unimorphisms of X.
DOI : 10.4064/cm-74-1-109-121
Keywords: real-valued measurable cardinal, invariant measure, Haar measure, locally compact space

Piotr Zakrzewski 1

1 
@article{10_4064_cm_74_1_109_121,
     author = {Piotr Zakrzewski},
     title = {The uniqueness of {Haar} measure and set theory},
     journal = {Colloquium Mathematicum},
     pages = {109--121},
     year = {1997},
     volume = {74},
     number = {1},
     doi = {10.4064/cm-74-1-109-121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-74-1-109-121/}
}
TY  - JOUR
AU  - Piotr Zakrzewski
TI  - The uniqueness of Haar measure and set theory
JO  - Colloquium Mathematicum
PY  - 1997
SP  - 109
EP  - 121
VL  - 74
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-74-1-109-121/
DO  - 10.4064/cm-74-1-109-121
LA  - en
ID  - 10_4064_cm_74_1_109_121
ER  - 
%0 Journal Article
%A Piotr Zakrzewski
%T The uniqueness of Haar measure and set theory
%J Colloquium Mathematicum
%D 1997
%P 109-121
%V 74
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-74-1-109-121/
%R 10.4064/cm-74-1-109-121
%G en
%F 10_4064_cm_74_1_109_121
Piotr Zakrzewski. The uniqueness of Haar measure and set theory. Colloquium Mathematicum, Tome 74 (1997) no. 1, pp. 109-121. doi: 10.4064/cm-74-1-109-121

Cité par Sources :