# Samuel Lockman: Kolmogorov’s Theorem, Haar Functions and Brownian Motion — A Measure Theoretic Introduction

## Bachelor thesis presentation

**Time: **
Tue 2022-08-23 09.00 - 10.00

**Location: **
Albano, House 1, Room N

**Respondent: **
Samuel Lockman

**Abstract:**

In this text, we seek to give a measure theoretic introduction to Brownian Motion and prove two of its main properties. Part of it is done through the continuity theorem of Kolmogorov, which in itself can be considered a central result. Furthermore, the paper also includes a construction of a Brownian motion via the Haar functions by first proving it is an orthonormal basis of \( L^2 [0, 1]\).