I am about to take a real analysis course and i wanna ask if anyone can provide some good texts or reference or any other source. The lectuer indeed suggested the Rudin real and complex analysis but i wonder if there are more and better texts and sources. The course content are provided as follows.Thx
Course content:
Lebesgue Measure on $\mathbb{R}$: Measurable sets and Lebesgue measure, Measurable functions
The Lebesgue Integral: The Lebesgue integral, modes of convergence
Differentiation and Integration: Functions of bounded variation, Differentiation of an integral, absolute continuity
General Measure and Integration Theory: Measurable spaces, measurable functions, integration, convergence theorems, the Radon-Nikodym theorem
The $L^p$ Spaces: The $L^p$ spaces, convergence and completeness, bounded linear functionals