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mahler1
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Homework Statement
Let ##E \subset \mathbb R^n## be a measurable set such that ##E=A \cup B## with ##|B|=0## (##B## is a null set). Show that ##A## is measurable.
The Attempt at a Solution
I know that given ##\epsilon##, there exists a ##\sigma##-elementary set ##H## such that ##E \subset H## and ##m_e(H-E)<\epsilon##. How can I construct a ##\sigma-##elementary set ##H'## such that ##m_e(H-A)<\epsilon##?. Any suggestions would be appreciated
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