Solovay showed that assuming the negation of the axiom of choice, there exists a model of real analysis where all sets are measurable. So really you only need m

Solovay showed that assuming the negation of the axiom of choice, there exists a model of real analysis where all sets are measurable. So really you only need measure theory if the paper depends on the axiom of choice in some fundamental way. But would you really trust an economics paper that depended on the axiom of choice? For me, a good analogy is with engineers and real numbers. Engineers use real analysis all the time. But the results of an engineering paper should not depend on the definition of a real number, nor should the engineer care. Edit: Hamming made the point better than I can: "Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane".