John
Reputation
1,250
Next privilege 2,000 Rep.
 Nov29 comment Is this definition missing some assumptions? This was asked before: math.stackexchange.com/questions/127616/… Nov29 awarded Citizen Patrol Nov29 revised Problem 3-38 in Spivak´s Calculus on Manifolds link to post added Nov29 revised An application of partitions of unity: integrating over open sets. link to post added Nov28 revised Problem 3-38 in Spivak´s Calculus on Manifolds tag added Nov27 revised Problem 3-38 in Spivak´s Calculus on Manifolds word change Nov27 asked Problem 3-38 in Spivak´s Calculus on Manifolds Nov27 accepted Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Answer aded Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Explanation added Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Image added Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Remark added Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Remark added Nov25 answered Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Nov25 comment Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? The definition of integral used in the problem involves partitions of unity and absolute convergence of a certain series, and may not coincide with the usual one. See p.65 of the book. Is that the integral you have in mind? Because you don´t mention partitions of unity at all. Nov25 comment Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? I stated the problem exactly as it is the book. I know there is no need for additional asumptions to show that the integral does not exist. Also given the fact that Spivak explicitly says "$f(x)=0$ for $x\not\in$ any $A_{n}$" I am inclined to think that he meant that $n\ge 1$. Nov25 revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? sentence change Nov25 asked Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? Nov24 answered An application of partitions of unity: integrating over open sets. Nov23 accepted Solving problem 3-29 in Spivak´s Calculus on Manifolds without using change of variables