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Consider the following result: A: Let $f:D \to \mathbb R$ be an increasing function with discontinuities on a dense countable subset of $D$ such that the jump values sum to $\mu(D)$, where $D$ is a ...

Definition: a function $f:\mathbb{R}\to \mathbb{R}$ has Luzin-(N)-Property if $f$ maps any null set to a null set. By https://www.encyclopediaofmath.org/index.php/Luzin-N-property, it is known that ...

One might say, "a random subset of $\mathbb{R}$ is not Lebesgue measurable" without really thinking about it. But if we unpack the standard definitions of all those terms (and work in ZFC), it's not ...

Let $f(x,u): [0,1]^2 \mapsto \mathbb{R}$ be a continuous function. [Q] Is $g(x) = \inf_{u\in [0,1]} f(x,u)$ always Borel measurable? If not, can one find a counter-example? Note that, for any $c$, ...