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This course covers the basic facts from probability in a measure-theoretic approach.

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Refresher in Probability 1. Refresher in Probability 2. Finance course News: There is a block course in the last week before the lecture regularly starts, so from 10th of Oct.

Probability and Measure Theory

The schedule is as follow: Mon. Contents: This course covers the basic facts from probability in a measure-theoretic approach.

Specific topics are Definition and properties of measure and Lebesgue integral. The fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem. At the end of the course, the student is able to: 1 describe elementary notions as area and volume in terms of measures.

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Probability and Measure offers a general approach to the theory of integration based on measure theory. This is a far reaching extension of the well known theory of Riemann integration. The approach via measures provides a wide variety of applications: in particular about the interchange of various limiting procedures.

Probability and Measure Theory | Statistical Science

The development via measurable functions is inspired by probability theory. It provides the necessary basis for a rigorous understanding of stochastic processes. Also, a connection with functional analysis is provided via the introduction of spaces of Lebesgue integrable functions. Rodrigues Valesin, PhD. In the Analysis course, students are also expected to have acquired the ability of explaining and elaborating mathematical proofs.

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