Question: { A s s u m e } f : f : E R with E measurable and m ( ) < m ( E

{Assume}
f
:
f:ER with
E measurable and
m
(
)
<
m(E)<, then for simple functions
g
,
h
g,h with
g
f
h
gfhon
E,??
oindenttextit{Prove} that:
g
(
)
f
(
)
f
h
.
E
g(L)
E
f(U)
E
f
E
h.
In particular, if
f
(
)
[
c
,
d
]
f(E)[c,d], then:
c
m
(
)
(
)
f
(
)
f
d
m
(
)
.
cm(E)(L)
E
f(U)
E
fdm(E).

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