Let A and B be two disjoint sets in the interval (0,1) . Denoting by μ the Lebesgue measure on the real line, let μ(A)>0 and μ(B)>0 . Let further n be a positive integer and \lambda \equal{}\frac1n . Show that there exists a subinterval (c,d) of (0,1) for which \mu(A\cap (c,d))\equal{}\lambda \mu(A) and \mu(B\cap (c,d))\equal{}\lambda \mu(B) . Show further that this is not true if λ is not of the form n1. real analysisreal analysis unsolvedcollege contestsMiklos Schweitzer