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

$\mathbb{R}^{n}$ 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.