Measure theory

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Delivered by Gregory Patchell on Friday October 28, 2016

The first part of this talk will be concerned with a brief introduction to measure theory. We will answer questions such a: How do we measure sets? Can every set be measured?

The second part of this talk will be the construction of the Lebesgue integral along with basic properties of the Lebesgue integral, along with comparisons to Riemann integration as we go. From Math 148, we saw that pointwise convergence doesn’t play well with Riemann integration. We will see that with the powerful Monotone Convergence Theorem and the Dominated Convergence Theorem, pointwise convergence and Lebesgue integration are a match made in heaven.


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