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

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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. http://geodesic.mathdoc.fr/articles/10.4064/cm-81-2-157-160/

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