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



Let

f

be a continuous function on

0,1

that is absolutely continuous on

\epsi lon,1

for each

0<\epsi lon<1

. (i) Show that

f

may not be absolutely continuous on

0,1

. (ii) Show that

f

is absolutely continuous on

0,1

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

f

on

0,1

, defined by

f(x)=\sqrt(x)

for

0<=x<=1

, is absolutely continuous, but not Lipschitz, on

0,1

.



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