Equipartition of a Segment

We prove that, for any positive integer m, a segment may be partitioned into m possibly degenerate or empty segments with equal values of a continuous function f evaluated on segments, assuming that f may take positive and negative values, but its value on degenerate or empty segments is zero.

Funding: S. Avvakumov’s research was supported by the European Research Council under the European Union’s Seventh Framework Programme [ERC Grant StG 716424–CASe]. R. Karasev’s research was partially supported by the Russian Foundation for Basic Research [Grant 19-01-00169].