The ham-sandwich theorem is famous as an application of Borsuk's antipodal theorem. It states that given n measurable sets A₁,. . . , Aₙ with positive Lebesgue measure in Rⁿ, it is possible to divide each one of them in half by a hyperplane. Recently the author applied Borsuk's antipodal theorem to optimization theory in 3. In this paper we extend the ham-sandwich theorem to some ratio not in half by using the technique of 3.
Hidefumi Kawasaki (Mon,) studied this question.