1,215 reputation
419
bio website
location
age
visits member for 2 years, 2 months
seen Jan 16 at 15:16

Nov
29
comment Is this definition missing some assumptions?
This was asked before: math.stackexchange.com/questions/127616/…
Nov
29
awarded  Citizen Patrol
Nov
29
revised Problem 3-38 in Spivak´s Calculus on Manifolds
link to post added
Nov
29
revised An application of partitions of unity: integrating over open sets.
link to post added
Nov
28
revised Problem 3-38 in Spivak´s Calculus on Manifolds
tag added
Nov
27
revised Problem 3-38 in Spivak´s Calculus on Manifolds
word change
Nov
27
asked Problem 3-38 in Spivak´s Calculus on Manifolds
Nov
27
accepted Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Answer aded
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Explanation added
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Image added
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Remark added
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Remark added
Nov
25
answered Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Nov
25
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.
Nov
25
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 $n\ge 1$.
Nov
25
revised Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
sentence change
Nov
25
asked Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds?
Nov
24
answered An application of partitions of unity: integrating over open sets.
Nov
23
accepted Solving problem 3-29 in Spivak´s Calculus on Manifolds without using change of variables