Advice needed on learning measure theory.

[funcalys]

Do you think having Bogachev's Measure Theory (vol. I) as a first exposure to measure theory sounds a good idea?
I mean while I can understand well the concepts presented in the book, I find some techniques used in the proof section quite hard to follow.

 

[justinmir]

FYI - http://www.essex.ac.uk/maths/people/fremlin/mt.htm - I have not read it myself and don't know how well it is written.
I read "Measure Theory" by Paul Halmos and found it extremely well written.

 

[homeomorphic]

Try A Radical Approach to Lebesgue's Theory of Integration. It has a very good historical prelude to measure theory, going up to Chapter 7, after which you can read other textbooks and it will be much better motivated.

 

[Jorriss]

Try A Radical Approach to Lebesgue's Theory of Integration. It has a very good historical prelude to measure theory, going up to Chapter 7, after which you can read other textbooks and it will be much better motivated.

That book looks awesome. I think I'm going to get that too.

 

[rezeew]

I would recommend approaching the learning of measure theory with a combination of resources and techniques. While Bogachev's Measure Theory (vol. I) may provide a comprehensive and rigorous introduction to the subject, it may not be the most accessible or user-friendly resource for a first exposure.

I would suggest supplementing your learning with additional resources, such as online lectures, video tutorials, or other textbooks that may present the material in a more approachable manner. Additionally, actively engaging with the material by attempting practice problems and seeking clarification from a professor or tutor can greatly enhance your understanding and retention of the concepts.

It is also important to keep in mind that measure theory is a complex and abstract subject, and it is normal to struggle with some of the techniques used in proofs. It takes time and practice to develop proficiency in this area, so do not be discouraged if you find certain aspects challenging.

In summary, while Bogachev's Measure Theory (vol. I) may be a valuable resource, it may be beneficial to supplement your learning with other materials and actively engage with the material to fully grasp the concepts. Ultimately, the most important factor in successfully learning measure theory is finding a method that works best for you.