- #1

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If f is a strictly increasing function, then f is Borel measurable.

Proof:

Let [itex]H=\{x \in \mathbb{R} : f(x) > \alpha \}[/itex]. I want to show that [itex](\alpha, \infty) \subset H[/itex].

My first guess is to assume that this is non-empty or else the result is trivial.

The next step, from a hint I was given, was to look at infimums (or supremums). However, I'm not sure how to proceed.