About the project

Probability space is a website devoted to probability theory, which is a mathematical field concerned with the study of random phenomena. This website will present the modern, measure-theoretic probability theory and will cover key topics like random variables, expectation, independence, laws of large numbers, and the central limit theorem.

If you are interested how it is possible to derive a mathematical theory for phenomena that are unpredictable, you are at the right place. You can already download the mathematical content while the website is under construction.

The file size is 1.3 MB.

About the writer

My name is Nikolai and I obtained my Master's degree in mathematics at ETH Zurich. I had the great opportunity to attend lectures of the Probability Theory Group, which consisted of the professors Alain-Sol Sznitman, Vincent Tassion, and Wendelin Werner. After my graduation I continued to devote time to mathematics and started to compile my personal overview of probability theory.

This project is mostly driven by a subjective reason. I think the mathematical objects and results in probability theory are beautiful. I decided to share my work hoping that you will find it useful and that I can present the subject in a way that will make it resonate with you the same way it resonates with me.

Goals

The first goal of this project is to derive the mathematical theory rigorously and to motivate and illustrate as much as possible. On the one hand, I present detailed proofs and mention the "obvious" steps, so that the reader can follow the mathematical arguments more easily. On the other hand, I motivate every topic, provide examples and try to explain why we proceed in the way we do.

The second goal of this project is to make the learning experience more appealing. Since the content will be hosted on a website, interactive features will let the reader engage with it in a way that cannot be achieved with a print version.

Support this project

The content is free, but the information is priceless. If you like this project, I would like to encourage you to share this website with your friends and colleagues. You may also support this project by a donation. Simply click the button below to donate an amount of your choice. Your support is much appreciated!

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Contact

I have written the mathematical content with a great attention to detail and have reviewed it very carefully, but it is entirely possible that it contains typos or mistakes. If you find a mistake, please let me know. You are also kindly invited to send me an email if you want to reach out to me for another reason.

Next steps

The website containing the mathematical content will be published next. I genuinely enjoy to prepare the material for this website and I am excited to share it with you. It is my goal to add new chapters and to extend existing ones so that this website will grow. Keep an eye out for updates!