 I've never had a measure theory class in graduate school, and so this was mostly for self-learning. I wanted to know a little bit more about this field, so I picked up this book. The contents of the book are somewhat brief, there's 15 chapters, and I'm still working through the book, so it's a book I haven't quite finished yet. I've been really impressed with the motivation it gives for measure theory. That's something I've always been curious about. I've always felt that with the axioms of probability, I had a very good foundation for the rest of my life. What else could there be? The authors address this right at the beginning. They give an answer for the motivation for measure theory. Now I'm not going to get into the author's arguments here, I can save that for another time. I just wanted to highlight that the book did a really good job knowing where I was at at least, and maybe other readers feel the same when it comes to measure theory. Something else that surprised me was the concept of a probability triple. I've read so many statistic books, and I have never come across a probability triple. Maybe I just overlooked it, or I wasn't reading carefully. This book made the probability triple its own topic. I thought the description was thorough and fantastic. I was able to follow along pretty well, and again, this is coming from someone who hasn't had formal education in measure theory. I was very impressed with how well the book laid out the content so that I could follow it. After laying the foundations, the book then goes into some content that I am a lot more familiar with. Ideas are random variables, for example. I wouldn't say that I was too surprised by the content, but I was able to think about it in the context of the broader ideas of measure theory and probability triples. I've never heard of tail fields before. This is a new idea. Expected values is one of the most common things covered in a statistics book, and this book goes fairly deep into expected values. Chapter 5 hits inequalities and convergence. Convergence isn't, again, one of those topics that I am a little understudied on, but I am aware of a few inequalities that are useful for probability and statistics. And this is about as far as I've made it in the book. Some of the other things that I've seen as I looked ahead was ideas around stochastic processes. A while ago, I read a book. I think it was called Stochastic Processes in R. I become a little bit familiar with stochastic processes. It's something that I don't really deal with too often. So personally, I'm not too interested in stochastic processes. Markov chains, I think, are interesting. The main chain I'm familiar with is Markov chain Monte Carlo, the chains that you commonly see in Bayesian computation. Chapter 11 talks about characteristic functions, and this is a topic that's a big deal, characteristic functions, moment generating functions, cumulant functions. These are all trist ways of expressing probability distributions, and they have a lot more functions than this, but that's also a topic for another video. Of course, this book goes into much more depth than I'm used to. This book also covers Martin Gales, and this is something I really wanted to become a little bit more familiar with. It's a subject I don't know too much about. I know it's a big deal in theoretical probability or measure theory, and so I was really happy to see it in this section. In fact, having a dedicated space for it was one of the main reasons I bought the book. Overall, some reasons that I've enjoyed this book so far is that I love the idea of probability triples. That was such an eye-opening concept for me, a very parsimonious way to describe the tools of a probability measure, and I'm excited to get into the Martin Gales. So from my opinion, this book has been better than a lots of the free online measure theory that I've read. I think it provides a lot more motivation for ideas, and sometimes the motivation is what keeps me going. I'm not sure if you've had an experience where maybe you read a Wikipedia page and you're just left wondering why is this even important? Why is this even a concept worth covering? And I felt a lot more comfortable with the motivation for the ideas after reading this book, and that's it. Thanks for watching.