# $\mathbb{R}^{n}$ analysis book that uses Lebesgue integrals

A professor told me it would be unwise to study an $\mathbb{R}^{n}$ analysis book that uses Riemann integral. However, I do not know any book that doesn't. Is there something that covers material similar to Spivak's Calculus on Manifolds, but using Lebesgue integrals instead? I don't think these topics are generally covered in a measure theory book.