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A function f is said to be Borel measurable provided its domain E is a Borel...

A function f is said to be Borel measurable provided its domain E is a Borel set and for each c, the set {x in E l f(x) > c} is a Borel set. Prove that if f and g are Borel measurable functions that are defined on E and are finite almost everywhere on E, then for any real numbers a and b, af+bg is measurable on E and fg is measurable on E.

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