Re: Range of the averages convex?


"johnson" <johnson246@xxxxxxxxxxx> wrote in message
news:sm9Wg.2203$e65.1080@xxxxxxxxxxx
Let f be an essentially bounded Lebesgue measurable function on [0,1].
Consider the set
\int_E f d\mu
where \mu is the Lebesgue measure and E are Lebesgue measurable subsets of
[0,1].
Must f be convex?

Correction:

Let f be an essentially bounded Lebesgue measurable function on [0,1].
Consider the set S=
\int_E f d\mu
where \mu is the Lebesgue measure and E are Lebesgue measurable subsets of
[0,1].
Must S be convex?


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