On a functional equation with asymptotically unique continuous solutions. (Short Communication).
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 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.