Carathéodory's Theorem Proof - Part 1/2 | Measure Theory

The first part of proving Caratéodory's Theorem. We prove that the set M defined in the theorem is a sigma-Algebra. ☕ Make a small donation on Ko-fi: https://ko-fi.com/problemathic 📚 Buy measure theory books: Folland - Real Analysis: https://amzn.to/3Qnjjme Wheeden Zygmund - Measure and Integral: https://amzn.to/3SuZYC7 Tao - An introduction to measure theory: https://amzn.to/47AS7aH Stein - Real Analysis: https://amzn.to/3QiEfdY 💸 Support us on Patreon, get great perks and items!   / problemathic   👕 Buy great math t-shirts! https://problemathic.creator-spring.com/ 💥 Over 40k followers on Instagram, join us!   / problemathicvideos   💬 Join our Discord server!!   / discord   🖇️ https://linktr.ee/Problemathic Timestamps in this video: 00:00 Introduction. 01:00 X is measurable. 02:02 Closed under complementation. 04:13 Closed under countable unions. 10:00 Countable unions of disjoint sets. 18:13 Conclusion. #maths #measuretheory #analysis