Measure Theory

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Anonymous

Measure Theory 2016-01-16 12:43:42 Post No. 7787723

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Measure Theory 2016-01-16 12:43:42 Post No. 7787723

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Tell me everything I need to know about measure theory.

>>

>>7787723

Measures exist.

>>

A few things to look up

Definition of a sigma-algebra, of a measure, of a measurable function.

Some constructions (product measures, push-forward, Caratheodory)

Properties of the Lebesgue measure (regularity, behaviour under diffeomorphism)

Construction of the integral relative to a measure

Lp spaces

Riesz representation theorems

Radon-Nikodym theorem

>>

depends what you need it for. if you only want to know the gist of it to bring it up in your autistic name-droppings, you have to realize that it is a way to formalize the whole aspect of "defining length", and from there, the fields of probability, integration, analysis fall out.

For example, you can learn a good amount of Markov Chains without knowing measure and freely using Fubini to justify interchange of integral and summation(for integrable functions).

its a very dry field and you start from "basics"(sigma algebra, borel sets), and work from the ground up. so you could follow what >>7787761

said.

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