Lecture 7: Sigma Algebras

MIT 18.102 Introduction to Functional Analysis, Spring 2021
Instructor: Dr. Casey Rodriguez

Last time, we introduced outer measures, which have most properties we want for a measure. We define Lebesgue measurable sets and ultimately the Lebesgue measure. We also define sigma-algebras, including the important Borel sigma-algebra.

License: Creative Commons BY-NC-SA

[aaronrobertcattell]

An abbreviation is a shortening of a word or a phrase. An acronym is an abbreviation that forms a word. An initialism is an abbreviation that uses the first letter of each word in the phrase (thus, some but not all initialisms are acronyms).

[SSNewberry]

This mainly about definitions and the intricacies of proving what seems to be obvious but is not. Extremely fine attack.

[cristianismopuroesimples]

Excelente, quem estuda análise bayesiana, é imprescindível aprender sigma-algebra

[kingarthr]

Alpha algebras are afraid of sigma algebras

[sunritroykarmakar]

Instead of the compactness argument at 21:00 why cant we consider (a + e/2, b- e/2) is a subset of I so the lower bound on the outer measure of I is b-a - epsilon

[carl]

100:28 is it simpler to say E \in A => E^c \in A, so R = E u E^c \in A, so ø = R^c \in A ? (i.e. more direct from initial axioms)

[tuongnguyen]

I thought this was some measure theory stuff :))) but some how it goes into functional analysis

[joenissan]

Exactly what is this used for? When would this be used in life?