Current / Reference edition

• Existing: Seminar 04 — Lp spaces and inequalities — working note
• Next: Week 05 — Duality of Lp
• Reference edition assumption: Real Analysis: Modern Techniques and Their Applications, 2nd edition (1999), ISBN 9780471317166. The existing notes do not specify the edition or printing.
• Edition / chapter-order source: Wiley publisher catalogue
• Printing check / errata: author’s book errata page
• TODO: Check the edition, printing, table of contents on pp. xiii–xiv, and section numbers against your copy.
• Scope: Follow the main chapters from §6.2 through §11.4. Complete exercise solutions and each chapter’s Notes and References are not assigned separate weeks.
• Workload: Plan 150–165 minutes per week, with prerequisites checked separately before the presentation.
• Checklist of unverified prerequisites

Study order / Dependency

• §6.2 duality → §6.3 integral inequalities → §6.4 weak Lp → §6.5 interpolation
• Chapter 7 Radon measures → Chapter 8 Fourier analysis → Chapter 9 distributions / Sobolev spaces
• Chapter 10 probability → Chapter 11 further measures and integration
• Dependency: Chapters 1–3 / §7.4 / §8.6 → Chapter 10; Chapters 1 / 4 / 7 → Chapter 11
• TODO: Distinguish reading order from the actual prerequisites of each theorem in every week.

Ordered Weeks

Week	Main topic	Reference section	Seminar
05	Duality of Lp	§6.2 Part I	165 min
06	Lp Duality — Endpoints and Consequences	§6.2 Part II	150 min
07	Integral Inequalities and Kernel Operators	§6.3 Part I	150 min
08	Homogeneous Kernels and Hardy Inequalities	§6.3 Part II	150 min
09	Distribution Functions and Weak Lp	§6.4	150 min
10	Riesz–Thorin Interpolation	§6.5 Part I	165 min
11	Marcinkiewicz Interpolation	§6.5 Part II	165 min
12	Radon Representation — Measure Construction	§7.1 Part I	165 min
13	Radon Representation — Integral and Uniqueness	§7.1 Part II	150 min
14	Radon Regularity and Approximation	§7.2	150 min
15	The Dual of C0	§7.3	165 min
16	Products of Radon Measures	§7.4	150 min
17	Fourier Preliminaries and Convolution	§8.1; 8.2 Part I	150 min
18	Approximate Identities and Smooth Approximation	§8.2 Part II	165 min
19	Fourier Transform on L1 and Schwartz Space	§8.3 Part I	150 min
20	Fourier Inversion and Plancherel	§8.3 Part II	165 min
21	Periodization and Summation of Fourier Integrals	§8.3 Part III; 8.4 Part I	165 min
22	Summation of Fourier Series	§8.4 Part II	150 min
23	Pointwise Fourier Convergence — Localization	§8.5 Part I	165 min
24	Pointwise Fourier Convergence — Limits of the Theory	§8.5 Part II	150 min
25	Fourier Analysis of Measures	§8.6	150 min
26	Fourier Methods for PDE — Poisson and Heat Kernels	§8.7 Part I	165 min
27	Fourier Methods for PDE — Wave Equation	§8.7 Part II	150 min
28	Distributions — Test Functions and Derivatives	§9.1 Part I	150 min
29	Distributions — Localization and Regularization	§9.1 Part II	165 min
30	Compactly Supported Distributions	§9.2 Part I	165 min
31	Tempered Distributions and Fourier Transform	§9.2 Part II	165 min
32	Periodic Distributions and Fourier Coefficients	§9.2 Part III	150 min
33	Sobolev Spaces — Fourier and Hilbert Structure	§9.3 Part I	165 min
34	Sobolev Embedding and Localization	§9.3 Part II	165 min
35	Elliptic Regularity in Sobolev Spaces	§9.3 Part III	165 min
36	Probability — Measure and Independence	§10.1	150 min
37	Laws of Large Numbers — Weak Law and Maximal Estimate	§10.2 Part I	150 min
38	Strong Law of Large Numbers	§10.2 Part II	165 min
39	Central Limit Theorem	§10.3	150 min
40	Construction of Sample Spaces	§10.4	150 min
41	Wiener Process — Gaussian Construction	§10.5 Part I	150 min
42	Wiener Process — Continuous Paths	§10.5 Part II	165 min
43	Haar Measure — Existence	§11.1 Part I	165 min
44	Haar Measure — Uniqueness and Modular Function	§11.1 Part II	165 min
45	Hausdorff Measure and Dimension	§11.2 Part I	150 min
46	Hausdorff Measure on Submanifolds	§11.2 Part II	165 min
47	Self-Similarity and Dimension	§11.3	165 min
48	Integration on Manifolds	§11.4	150 min

Cross-reference

• Linear Algebra Review
• Saad
• Study Roadmap