MathDB
measurablility of level sets

Source: Miklos Schweitzer 2006 q8

September 14, 2021
real analysis

Problem Statement

let f(x)=∑n=0∞2−n∣∣2nx∣∣f(x) = \sum_{n=0}^{\infty} 2^{-n} ||2^n x|| , where ||x|| is the distance between x and the closest integer to x. Are the level sets {x∈[0,1]:f(x)=y}\{ x \in [0,1] : f(x)=y \} Lebesgue measurable for almost all y∈f(R)y \in f(R)?
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