Miklos Schweitzer 1963_9
Source:
September 19, 2008
functionreal analysisgeometrytrapezoidreal analysis unsolved
Problem Statement
Let be a continuous function on the interval , 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 is Lebesgue-measurable, and find the minimum of its measure with respect to all functions . [A. Csaszar]