Show that there is a set E of measure zero such that g^(-1) [E] is not measurable
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Show that there is a set E of measure zero such that g^(-1) [E] is not measurable

[From: ] [author: ] [Date: 13-01-21] [Hit: ]
1], which is not measurable.......
Show that there is a set E of measure zero such that g^(-1) [E] is not measurable
Thanks for your help

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Let E be the rational numbers Q. Let g : [0,1] → R be such that g(x) = x if x is in Q, and g(x) = √2 if x is not in Q. Then g^(-1)[E] = Q ⋂ [0,1], which is not measurable.
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