I have self-studied mathematical analysis using books written by people from my country. These books cover traditional topics including green formula and stokes formula ($\mathbb{R}^3$ form). However,I want a more solid basis of multivariate analysis, so I'm looking for a book which that introduces multivariate analysis rigorously and comprehensively.
Also, I sometimes encounter the so-called divergence theorem(i.e. problems in Stein's Fourier analysis), which is the general form of stokes formula, and I would like the book to cover such kind of topics.
Is there any book that fit these requirements(using either Riemann or Lebesgue Integral)?