Talk:Measure Theory

Feedback welcome

Hi, this is clearly a little pet project of mine. I'm clearly designing this unlike the usual measure theory course by trying to explain a lot of the history and context of the course, while also teaching the content. I believe, or at least hope, that this will help some newcomers to the subject.

I am more or less writing it all off the top of my head, and therefore I'm bound to make mistakes, miscalculations, misquote things. I welcome feedback and edits that are consistent with my design -- but really hope that I'll be free to build this thing in my own quirky way. Addemf (discuss • contribs) 00:47, 27 December 2023 (UTC)

Specific to General or General to Specific

I chose to develop this course by starting from Lebesgue theory, with the intent to later generalize to measure theory. A lot of mathematicians dislike this direction of explanation, and think that it's better to go from general to specific instead. I want to go ahead and present my reason for not preferring to teach that way.

Mathematicians do organize the knowledge in their own head, flowing from the general to the specific. But this only makes sense when you already know what the general theory can apply to -- if you learn the generality first, you don't have the details and context which tells you why these things matter. It makes abstract objects pop into existence as if they come out of thin air.

It may feel like it takes longer, because you feel as though the generalization often involves a lot of repetition of earlier material. But if you factor in the time that students spend trying to make sense of the generality when it lacks helpful details, I suspect that students learn better and faster by starting from the more concrete. Addemf (discuss • contribs) 02:21, 1 January 2024 (UTC)

To-Do

• Summarize each lesson with a list of theorems proved in it.

• Add cross-referencing links between lessons and also to other proof sources.

• Add a generalization to general measures.

Addemf (discuss • contribs) 19:10, 30 January 2024 (UTC)

• Check each proof to make sure it considers the case of infinite measures and infinite integrals.

Addemf (discuss • contribs) 17:41, 31 January 2024 (UTC)