MathDB
Miklos Schweitzer 1963_9

Source:

September 19, 2008
functionreal analysisgeometrytrapezoidreal analysis unsolved

Problem Statement

Let f(t) f(t) be a continuous function on the interval 0t1 0 \leq t \leq 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 \overline{A_tB_t} is Lebesgue-measurable, and find the minimum of its measure with respect to all functions f f. [A. Csaszar]