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Measure Theory (14/15) - Lebesgue outer measure and Lebesgue measure on the real line (2/2)

The sigma-algebra of Lebesgue measurable sets. Lebesgue measure λ (on the Lebesgue measurable sets or on the Borel sets). Further properties of Lebesgue measure λ and Lebesgue outer…

From  Joel Feinstein 0 likes 14 plays 0  

Measure Theory (13/15) - Lebesgue outer measure and Lebesgue measure on the real line (1/2)

Brief discussion of the following: what we hope to achieve when measuring length, area and volume; the Banach-Tarski paradox; the Carathéodory extension theorem. The definition of Lebesgue…

From  Joel Feinstein 0 likes 10 plays 0  

Measure Theory (12/15) - Properties of measures (2/2)

Proofs of the continuity properties of measures for nested increasing unions and nested decreasing intersections of sequences of measurable sets. For more information and links to further resources,…

From  Joel Feinstein 0 likes 12 plays 0