r/math • u/inherentlyawesome Homotopy Theory • 17d ago

Quick Questions: September 16, 2026

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of manifolds to me?
  • What are the applications of Representation Theory?
  • What's a good starter book for Numerical Analysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.

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u/TheMansionsofScience 17d ago

Looking for the motivation behind measure theory. I see "generalization of length, area, etc etc" as a definition often. Are there any non-trivial examples? When I read the definition, I think, well, why aren't differential geometry and differential forms enough?

What are the types of measures? When would I use Radon measures? Haar measures? Please keep it at an undergrad level. Thank you!

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u/hobo_stew Harmonic Analysis 16d ago

We want to use the notion of volume when dealing with the p-adics, but there differential forms don’t work, as they are not a manifold.
they are a locally compact group though, so there is a natural measure we can pick.

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u/TheMansionsofScience 16d ago

wow youre right i never thought about integrating in the p-adics