Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  361.28013
Autor:  Erdös, Paul; Mauldin, R.Daniel
Title:  The nonexistence of certain invariant measures. (In English)
Source:  Proc. Am. Math. Soc. 59, 321-322 (1976).
Review:  It is proved that on an uncountable group G there does not exist a non-zero, \sigma-finite countably additive measure which is left-invariant and defined on all subsets of G. There is an earlier proof of this result due to F. Terpe which, however, as was observed by J. C. Oxtoby, presupposes (a certain consequence of) the continuum hypothesis. The present proof is independent of the continuum hypothesis.
Reviewer:  S.G.Dani
Classif.:  * 28C10 Set functions and measures on topological groups
                   04A10 Ordinal and cardinal numbers; generalizations
                   28A25 Integration with respect to measures and other set functions

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag

Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.
Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry
Probabability Personalia About Paul Erdös Publication Year Home Page