Intro to Probability

uni zurich spring 2025

“Introduction to Probability” provides a foundation for probability theory. We cover essential theoretical backgrounds in set theory, analysis, measure theory, and integration. Fundamental probabilistic concepts such as probability spaces, random variables, and laws are introduced, culminating in the study of random vector convergence.

This self-contained, introductory course offers precisely the theoretical tools needed for a rigorous treatment of probability theory. It is designed to build the necessary framework for advanced studies in this field.

Contents

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  1. Sets and Order Structure
    1. Sets
    2. Order Structure of the Real Numbers
  2. Functions, Cardinality and Distance
    1. Functions
    2. Cardinality of Sets
    3. Open and Closed Sets in Real Coordinate Spaces
  3. Sequences
    1. Real-valued Sequences
  4. Measurable Spaces
    1. σ\sigma-Fields and Measurable Spaces
    2. σ\sigma-Fields generated by Families of Sets
    3. Borel Sets of Real Coordinate Spaces
  5. Measures
    1. The Notion of a Measure
    2. Point Measures
    3. Counting Measures
    4. Properties of a Measure