(Solved): Let f be a continuous function on 0,1 that is absolutely continuous on \epsi lon,1 for each 0<\ep ...

Let

be a continuous function on

that is absolutely continuous on

for each

. (i) Show that

may not be absolutely continuous on

. (ii) Show that

is absolutely continuous on

if it is increasing. (iii) Show that the function

on

, defined by

for

, is absolutely continuous, but not Lipschitz, on

.