Thursday, 20 June 2019

real analysis - Proving that f(x)=frac1x2lnx is Lebesgue measurable on (2,+infty)

I have that a set E is Lebesgue measurable if the outer measure:
μ(E)=infI1,...,Inμ(I),EI1I2,...In,Iiintervals



satisfy the three properties of measure.
Proving that f(x)=1x2lnx

is Lebesgue measurable would suggest that I must prove that the set f((2,+)) satisfies these properties. Is this correct, and how do I go about proving this? Maybe using the fact that the function is a continuous bijection and a map of an open set would also be open and this would be a subset of Borel- sigma algebra. Help ?

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