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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

6 votes

Set of real numbers with positive measure containing no midpoints

No, such a set cannot exist and one can prove this using Lebesgue Density Theorem and a simple pegionhole argument. Infact all points $x$ which are density points of $E$ will be a midpoint for some $y …
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