juanberrio8a

juanberrio8a

Answered

2022-06-27

I'm looking to show that 1 | x | n is not integrable on the subset of R n where | x | 1. It's easy to do on R , and I think I need to apply Fubini's theorem for the general case, but not sure how to do so in n-dimensional space. Thanks

Do you have a similar question?

Recalculate according to your conditions!

Answer & Explanation

knolsaadme

knolsaadme

Expert

2022-06-28Added 16 answers

Via some computation and Tonelli's theorem, we have for measurable f : R n [ 0 , ] that
R n f ( x ) d x = S n 1 0 f ( r ω ) r n 1 d r d S ( ω ) ,
where d S is "surface measure" on S n 1 . Now you can plug in f ( x ) = 1 | x | n χ { x : | x | 1 } and compute it's integral.

Still Have Questions?

Ask Your Question

Free Math Solver

Help you to address certain mathematical problems

Try Free Math SolverMath Solver Robot

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?