Lebesgue Integration: Cantor Set

In course

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Description

This lecture covers the construction of the Lebesgue function on the Cantor set, exploring the binary expansion and the uniqueness of the binary operation. It also delves into the properties of the function, such as strict increasing behavior and its characterization as points with only digits 0 and 2. The lecture concludes with a proof regarding the measurability of certain sets and the implications for the function's injectivity.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_qkwzkc3o

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Ontological neighbourhood

Mathematics

Analysis: Measure theory

Mathematical logic: Set theory

Topology: General topology

Logic

Classical logic: First-order logic

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