Video lectures on Real Analysis? One of the most annoying gaps in my math education is Real analysis. 

I tried hard, but all I could find are either Harvey Mudd College lectures or MathDoctorBob. The latter are too short and the former are in horrendous format, I can barely make out what is written on the blackboard. 

Ideally I'd like the lectures to cover topics such as proofs of continuity, differentiation, some main inequalities, $\limsup$ and $\liminf$, uniform/pointwise convergence and continuity, dominated and monotone convergence and maybe a bit more. 

So if anyone knows if this material is available online, I'd be quite grateful.
You can try: http://www.uccs.edu/math/student-resources/video-course-archive.html

They have a Real Analysis course listed, Math 533 Real Analysis I - Fall 2007. They are good, though not that challenging.

You may need to create a [free] account to view the videos.

If you really don't want to make an account the videos start with:

http://cmes.uccs.edu/Fall2007/Math533/pages/video3.html

and go up to /video24.html. There is, for some reason, no video 1 or 2.
1 http://ocw.aca.ntu.edu.tw/ntu-ocw/index.php/ocw/cou/104S115 real analysis 1 at National Taiwan University ( Called Calculus for math majors 1)

2 http://ocw.aca.ntu.edu.tw/ntu-ocw/index.php/ocw/cou/104S210 real analysis 2 at National Taiwan University ( Called Calculus for math majors 2)