- #1

jem05

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## Homework Statement

Let (X , M, m) be a certain measure space and {E

_{n}} sets in M with the property:

[tex]\underline{lim}[/tex] (E

_{k}) = [tex]\overline{lim}[/tex](E

_{k}) = E

prove that lim m(E

_{i}) exists and = m(E) as n approaches infinity.

## Homework Equations

## The Attempt at a Solution

i solved the problem, if it were given that m([tex]\bigcup[/tex]E

_{i}) is stirctly less that infinity, but i don't know how to overcome that problem since that was not given.

any help is appreciated.

thank you.

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