The content of these notes will follow closely to Durrett’s “Probability: Theory and Examples” and Patrick Billingsley’s “Probability and Measure”. The aim of these notes is to provide an abridged version of measure theoretic probability, such that it still presents key ideas without delving deep into theoreticals. The expectation is that the reader will supplement the notes with the texts mentioned above. Key exercises are also presented as a way for the reader to engage with the fundamental concepts of the material and are drawn from the texts above. The exercises have no solutions posted but many of these exercises have been answered on various online forums.
My personal expectation regarding the diffuculty level as presented in the notes is that it is reasonable for an advanced undergraduate, or early graduate student in math, statistics, or related fields, to grasp as an introduction to measure theoretic probability.