Displaying 61 – 80 of 1206

Showing per page

On a gap series of Mark Kac

Katusi Fukuyama (1999)

Colloquium Mathematicae

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 = 0 n - 1 f ( 2 k t ) 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.

Currently displaying 61 – 80 of 1206