Let $\mu_C$ be the Cantor distribution. That is, the unique distribution whose cumulative distribution function is the Cantor function. If we think of integration w.r.t. $\mu_C(x)$, that is, the differential $d\mu_C(x)$, can we represent this as the limit of $\phi_n(x)dx,$ where $\phi_n$ is a family of Lebesgue simple functions. If so, does anyone know of such a sequence $\phi_n$?
2026-04-13 02:52:54.1776048774
Cantor Measure as the Limit of Simple Functions
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