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(Solved): Problem 5: If E is a Lebesgue measurable set and A is any subset of R, then show that m(EA)+m ...
Problem 5: If
E
is a Lebesgue measurable set and
A
is any subset of
R
, then show that
m
∗
(
E
∩
A
)
+
m
∗
(
E
∪
A
)
=
m
∗
(
E
)
+
m
∗
(
A
)
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we need to use some properties of Lebesgue measure.Proof: we know that m(X ? Y) = m(X) + m(Y) - m(X ? Y)
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