User:Timhoooey

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[edit] About me

I'm an undergraduate student pursuing a degree in pure mathematics. Right now I'm fighting my way through Royden's Real Analysis and find Wikipedia to be a valuable resource for augmenting the sometimes austere examples in the book.

I try to point out math articles that I find lacking/confusing from the perspective of a student who is trying to learn the material. I also like to contribute to topics that I recently learned about, but only after I am sure that I understand them. I'm just a student, so please don't hesitate to correct/question any statements I make. I usually put my ideas in the talk pages unless I have a very clear idea about what I'm trying to say.

[edit] Math Problems I Can't Solve Using Wikipedia

This section lists the math problems that I have been unable to find enough information on Wikipedia to solve. There are two sections, open problems, or problems which I am currently stuck on, and resolved problems, or problems that I have found solutions to. This is relevant to Wikipedia because it will help the folks associated with the Mathematics WikiPoject gauge the depth of (a very limited portion of) the math coverage on Wikipedia as well as help article authors determine which content to include. Eventually, I will transfer any substantial contributions here (from both myself and others) to appropriate articles.

Please consider adding ideas/solutions to this section. Disclaimer: this is also a shameless attempt to get homework help.

[edit] Open problems

[edit] Resolved problems

  • Prove: If f,g are extended real-valued measurable functions then the product fg is measurable. [1]
This is true if A and B are measurable sets and {x*y: x in A, y in B} is measurable, but it seems like there should be an easier way to go about this. -Timhoooey 06:08, 14 October 2007 (UTC)
Solution: Since f\, is measurable, (f)^k\, is measurable for integer powers k. Since f,g\, are measurable, f+g\, is measurable. Then note that fg=\frac{1}{4}((f+g)^2+(f-g)^2)\,. This is it! Timhoooey 01:12, 15 October 2007 (UTC)
  • Show that a sequence x0,x1,x2... converges to a limit x if and only if every subsequence has a convergent subsequence that converges to x. [2]
I can't work out why we need every sub-sub sequence to be convergent. I thought there was convergence iff every subsequence was convergent - Timhoooey 06:08, 14 October 2007 (UTC)
This is true iff every subsequence is convergent to the limit. We don't need to consider sub-subsequences. Timhoooey 04:49, 31 October 2007 (UTC)

[edit] To Do

  • Find a proof that is not "trickological" for the following statement: f,g extended real valued measurable functions => fg is measurable. See Talk:Measurable function

[edit] Footnotes

  1. ^ Royden, chapter 3, problem 22a
  2. ^ Royden, chapter 2, problem 12

[edit] References

  • H.L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988