Could you please recommend some open courses on Real Analysis, mainly about Lebesgue measure and Lebesgue Integral? I am a Chinese student and will be enrolled in the course about Lebesgue integral. I want some open courses to help preview the course. A little bit content about functional analysis is okay.
Thank you!

You may find this useful for real analysis, and this for functional analysis.
Moreover, you can find more video courses here about some other topics in mathematics.
If Chinese is OK to you, this course from Shanghai Jiao Tong University is acessible.
