A Proof of Kakutani's Conjecture on Random Subdivision of Longest Intervals
A Proof of Kakutani's Conjecture on Random Subdivision of Longest Intervals
Choose a point at random, i.e., according to the uniform distribution, in the interval (0, 1). Next, choose a second point at random in the largest of the two subintervals into which (0, 1) is divided by the first point. Continue in this way, at the $n$th step choosing a …