Assume Z is a real valued random variable such that it's distribution has a density with respect to Lebesgue Measure (i.e. its Radon-Nikodym derivative w.r.t Lebesgue measure exists.) Then what is the characterization of measurable real valued functions G, such that the distribution of $G \circ Z$ has a density with respect to Lebesgue measure as well?
2026-02-23 20:43:28.1771879408
Characterization of measurable G such that $G \circ Z$ has a density with respect to Lebesgue Measure
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