On a gap series of Mark Kac

Fukuyama, Katusi. "On a gap series of Mark Kac." Colloquium Mathematicae 81.2 (1999): 157-160. <http://eudml.org/doc/210733>.

@article{Fukuyama1999,
abstract = {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.},
author = {Fukuyama, Katusi},
journal = {Colloquium Mathematicae},
keywords = {cocycles; gap theorem; central limit theorem; central limit theorem for dyadic transformations},
language = {eng},
number = {2},
pages = {157-160},
title = {On a gap series of Mark Kac},
url = {http://eudml.org/doc/210733},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Fukuyama, Katusi
TI - On a gap series of Mark Kac
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 157
EP - 160
AB - 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.
LA - eng
KW - cocycles; gap theorem; central limit theorem; central limit theorem for dyadic transformations
UR - http://eudml.org/doc/210733
ER -