Let f(t) be a continuous function on the interval 0≤t≤1, and define the two sets of points A_t\equal{}\{(t,0): t\in[0,1]\} , B_t\equal{}\{(f(t),1): t\in [0,1]\}. Show that the union of all segments AtBt is Lebesgue-measurable, and find the minimum of its measure with respect to all functions f. [A. Csaszar] functionreal analysisgeometrytrapezoidreal analysis unsolved