Geodesic
On a gap series of Mark Kac
Colloquium Mathematicum, Tome 81 (1999) no. 2, pp. 157-160

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of $n^{-1/2}\sum_{k=0}^{n-1} f(2^kt)$ vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.
DOI : 10.4064/cm-81-2-157-160
Keywords: cocycles, gap theorem, central limit theorem

Katusi Fukuyama 1

1 
@article{10_4064_cm_81_2_157_160,
     author = {Katusi Fukuyama},
     title = {On a gap series of {Mark} {Kac}},
     journal = {Colloquium Mathematicum},
     pages = {157--160},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {1999},
     doi = {10.4064/cm-81-2-157-160},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-81-2-157-160/}
}
TY  - JOUR
AU  - Katusi Fukuyama
TI  - On a gap series of Mark Kac
JO  - Colloquium Mathematicum
PY  - 1999
SP  - 157
EP  - 160
VL  - 81
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-81-2-157-160/
DO  - 10.4064/cm-81-2-157-160
LA  - en
ID  - 10_4064_cm_81_2_157_160
ER  - 
%0 Journal Article
%A Katusi Fukuyama
%T On a gap series of Mark Kac
%J Colloquium Mathematicum
%D 1999
%P 157-160
%V 81
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-81-2-157-160/
%R 10.4064/cm-81-2-157-160
%G en
%F 10_4064_cm_81_2_157_160
Katusi Fukuyama. On a gap series of Mark Kac. Colloquium Mathematicum, Tome 81 (1999) no. 2, pp. 157-160. doi: 10.4064/cm-81-2-157-160

Cité par Sources :