Claims

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1969_01_01_kemperman: Kemperman proves that every Lebesgue measurable real function with twice its value at a point at most the sum of its values at the next two equally spaced points is nondecreasing; refereed, the measurable case of the question.

1984_01_01_laczkovich: Proves that every real function with twice its value at a point at most the sum of its values at the next two equally spaced points is nondecreasing, with no regularity assumed; refereed, credited by the site, Lean by others.

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