Introduction to Real Analysis
Coursera
Coursera course: Introduction to Complex Analysis
More resources on Lebesgue Integration
mathworld.wolfram.com
MathWorld is a comprehensive online mathematics encyclopedia from Wolfram that provides clear definitions, explanations, and formulas for a wide range of topics, including Lebesgue integration. Each topic page includes key concepts, theorems, examples, and links to related material and references.
ocw.mit.edu
MIT OpenCourseWare (ocw.mit.edu) offers free, openly licensed MIT course materials across the curriculum, including mathematics, with lecture notes, videos, assignments, and exams. In the math sections, you’ll find Lebesgue integration covered in real analysis and measure theory courses, featuring lecture notes, examples, and problem sets.
terrytao.wordpress.com
Terence Tao's blog is a comprehensive math resource of rigorous expository posts, lecture notes, and problem discussions—covering measure theory and Lebesgue integration (along with probability, analysis, and other topics)—plus occasional research updates.