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Oct 29, 2019 at 13:18 comment added sayantankhan Thanks! I guess I was just looking at the problem the wrong way. And from the fact that $p$ is upper semicontinuous, it shouldn't be too hard to find explicitly find continuous functions that approximate the period as well.
Oct 29, 2019 at 13:10 vote accept sayantankhan
Oct 29, 2019 at 13:05 history answered Mateusz Kwaśnicki CC BY-SA 4.0