On a gap series of Mark Kac
Fukuyama, Katusi
Colloquium Mathematicae, Tome 79 (1999), p. 157-160 / Harvested from The Polish Digital Mathematics Library
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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∑k=0n-1f(2kt) 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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210733 
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     year = {1999},
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     zbl = {0946.60018},
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Fukuyama, Katusi. On a gap series of Mark Kac. Colloquium Mathematicae, Tome 79 (1999) pp. 157-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p157bwm/

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