Measure Theory, Functional Analysis, and The Lebesgue Integral for Undergraduates - Johnston

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0:00 Intro (LOWER VOL) BEFORE NEXT CH)
0:16 Preface/Contents
0:54 Section 1.1 Uncountable Sets
3:12 Section 1.2 Measure Theory
5:21 Section 1.3 Step Functions
6:17 Section 1.4 Limits: Can This Book Substitute a Course on Real Analysis
7:53 1.5 L¹ Space
8:38 Chapter 2: Lebesgue's vs Riemann's Integral
9:22 Application: Fourier Series
9:58 Chapter 3: Function Spaces
10:48 Application: Quantum Mechanics
11:39 Measure Theory
11:52 Application: Probability
12:06 Chapter 12: Hilbert Space Operators
13:00 Index
13:28 Closing Comments

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[MathematicalToolbox]

Earphone users beware after the intro!
I apologize for the lack of focus in many parts of the video as well.

[Adamrpg]

Nice rec! Looks like it would be my go-to reference if I needed it. Put on my Wish List [although my family never gets me anything on my wish list, they say it's all textbooks!]

[economicist]

Have you ever read Stein and Shakarchi's "Fourier Analysis"? It's the first of a four part series on Analysis (Fourier, Complex, Real/Measure, Functional) and it's highly praised by mathematics YouTuber Daniel Rubin. It (or the series) may be a good candidate for your Hall of Fame if you agree with his assessment. I've only just begun the series myself.

[mabm]

Awesome! another book to add to my "to study later" list.
I guess I'll have to make a review of my linear algebra soon, I forgot most of it and when I studied it back then I was young and not math-mature enough to approach the challenging and fun problems (that, and being a student with literally no time didn't helped that much lol). Now I just study this stuff just for the fun and enjoyment. I feel and I'm sure I'm missing some interesting topics out there.

Now, how about some Differential Geometry and Tensor analysis? these are a couple of topics I've been considering to attack. So far I know that I should go with Diff. Geo. first.

Anyway, thanks for the video. Keep it ℝ matey haha.

[bhermep]

His other book, “A Transition to Advanced Mathematics: A Survey Course” also looks excellent. Do you own that as well? Any thoughts on that one?

[meteor]

Can you confirm that this is the easiest book on measure theory ?

[Murat-fiff]

Best book about lebesgue integration is J. YEH’s real analysis