Notes

Here are some brief daily notes I wrote in 2023:

2023-01-01. The big five theorems of elementary functional analysis
2023-01-02. A proof of the strong law of large numbers
2023-01-03. A proof of the De Moivre–Laplace Central Limit Theorem
2023-01-04. The construction of a Vitali set
2023-01-05. The fundamental theorem of finitely generated abelian groups
2023-01-06. Constructing the Lebesgue measure
2023-01-07. Determining a measure
2023-01-08. Conditional expectation as Radon–Nikodym derivative
2023-01-09. Some prominent problem-solving patterns in probability proofs
2023-01-10. Some results on random permutations
2023-01-11. Tychonoff's theorem and Kelley's theorem
2023-01-12. The portmanteau lemma
2023-01-13. Introduction to complex analysis
2023-01-14. Selected proofs on measure theory
2023-01-15. Carathéodory's extension theorem
2023-01-16. Introduction to complex analysis continued
2023-01-17. Ergodic theorems
2023-01-18. Another proof of the strong law of large numbers
2023-01-19. Law of the iterated logarithm
2023-01-20. A proof of the weak law of large numbers
2023-02-04. Miscellaneous results involving countability
2023-02-05. Probability as expectation
2023-02-06. Intuition for the law of the iterated logarithm
2023-02-07. A bit about the simple random walk
2023-02-08. The tail of a random variable
2023-02-09. Two 0–1 laws