Скачать или смотреть Why is the outer measure of irrational numbers in [0, 1] is 1? Surprising measure of irrational no.

In this intriguing video, we explore the fascinating world of measure theory and delve into the surprising result of the set of irrational numbers in the interval [0, 1] is 1. Carathéodory's criterion—a fundamental concept in measure theory. Discover how Carathéodory's criterion provides a powerful method for determining the measurability of sets. We start by explaining the concept of outer measure and its significance in measuring the size of sets. We then focus on the set of irrational numbers and demonstrate how, despite its infinite nature, it possesses an outer measure of exactly 1 within the unit interval. We explore the criteria's implications, including its connection to outer measures and the construction of measures. Join us as we unravel the mathematical reasoning behind this intriguing result and gain a deeper understanding of the measure of irrational numbers.
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