Measuring E and f in Product Space of Borel Measures

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Show that if E is a Borel measurable subset of R, then {(x,y)| x-y is in E} is also measurable in the product space of Borel measures...

Also, if f is a measurable function, show that F(x,y)=f(x-y) is also measurable..
 
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In the meantime: What do you know about measurable sets in R^2 ?
 

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