Show that the Cantor function is a monotone, nondecreasing func... | Filo

39K views · 647 reactions | The Devil's Staircase, part of the West Highland Way, goes from Altnafeadh in Glencoe to Kinlochleven. Well worth the effort to climb up and look at the views. | Glencoe Heritage Trust, Scotland | Facebook

5.7K views · 326 reactions | This lovely video popped up on memories...

The Devil's Staircase - Glencoe Scotland

Let f:[0.1]→[0.1] be the Cantor-Vitali function and let Γ⊂[0.1]... | Filo

SOLVED: Problem 4: The Cantor set C is defined as follows. Remove the middle third, i.e. the interval (1/3,2/3), from the segment [0,1] obtaining the set C1 which consists of the two closed intervals [0, 1/3] and [2/3,1]. Next, remove the middle third part of these two intervals, leaving C2 = [0,1/9] U [2/9,3/9] U [6/9, 7/9] U [8/9,1] and so on. Now consider Cn = 40n1. For the function f(x) = Ic(z) x, compute f dp; [0,1] where p = m 02/9 is the sum of the Lebesgue measure and the Dirac measu