COVID-19 Update: Starting Mon, Mar 23, all lectures will move to online format.
Lectures will be prerecorded and uploaded to Box. Links to videos as well the lecture notes in PDF format will be posted on this page (accessible only to the students of this class).
14. |
Mon, Apr 27 |
[PDF] [Video] |
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Bounded linear functionals on $L^p$, general case |
13. |
Mon, Apr 20 |
[PDF] [Video] |
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Lebesgue-Radon-Nikodym Theorem [Chap 6 Sec 4.2] |
12. |
Fri, Apr 17 |
[PDF] [Video] |
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spaces revisited, orthogonal projections, Riesz Representation Theorem [based on Chap 4, Sec 4 and 5.1] |
11. |
Wed, Apr 15 |
[PDF] [Video] |
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Signed measures, total variations, singular and absolutely continuous measures [Chap 6 Sec 4.1, 4.2 (start)] |
10. |
Mon, Apr 13 |
[PDF] [Video] |
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Lebesgue-Stieltjes integral and Borel measures on $\mathbb{R}$ [Chap 6 Sec 3.3] |
9. |
Fri, Apr 10 |
[PDF] [Video] |
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Polar (or spherical) coordinates [Chap 6 Sec 3.2] |
8. |
Wed, Apr 8 |
[PDF] [Video] |
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Product measures, the Fubini theorem [Chap 6 Sec 3.1] |
7. |
Mon, Apr 6 |
[PDF] [Video] |
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Integration on a measure space, measurable functions, simple fifunctions, Convergence Theorems, $L^p$ spaces [Chap 6 Sec 2] |
6. |
Fri, Apr 3 |
[PDF] [Video] |
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Premeasures and Extension Theorem [Chap 6 Sec 1.3] |
5. |
Wed, Apr 1 |
[PDF] [Video] |
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Metric exterior measures, Regularity of Borel measures [Chap 6 Sec 1.2] |
4. |
Mon, Mar 30 |
[PDF] [Video] |
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Abstract measure spaces [Chap 6 Sec 1]; Exterior measures and Caratheodory’s theorem [Chap 6 Sec 1.1]; Metric exterior measures [Chap 6 Sec 1.2 (start)] |
3. |
Fri, Mar 27 |
[PDF] [Video] |
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Bounded linear functionals on $L^p$; Remark on Banach spaces and their duals |
2. |
Wed, Mar 25 |
[PDF] [Video] |
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$L^p$ spaces for different $p$’s; $L^\infty$ space; Bounded linear functionals on $L^p$ |
1. |
Mon, Mar 23 |
[PDF] [Video] |
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Jump functions, Differentiability of jump functions [Chap 3 Sec 3]; $L^p$ spaces, Young’s, Hölder’s, Minkowski’s inequalities; Completeness of $L^p$ (Riesz-Fischer) |