I’m just wondering if there’s a name for the function defined below.
Write $x$ uniquely in base 2 (i.e. not ending in an infinite string of ones) as $x = \sum_{k=0}^{\infty}\frac{x_k}{2^k}$. Define $f(x) = \sum_{k=0}^{\infty}\frac{x_{2k}}{2^k}$.
I’m not having luck with Google. The closest thing I get is the “dyadic transformation” function, which might be similar? Maybe it has something to do with Cantor functions? (Also apologies to mods as I have no idea how to tag this. The chosen tags are based on topics covered in a course where this example came from, so I’m hoping it looks familiar to someone in that area.)
Ultimately, I’m interested in what I can say about the integrability of this function, but first just trying to understand it.