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Sep
12 |
awarded | Popular Question |
Feb
15 |
awarded | Favorite Question |
Sep
8 |
awarded | Notable Question |
Sep
21 |
awarded | Popular Question |
Aug
16 |
awarded | Yearling |
Feb
19 |
awarded | Nice Question |
Sep
23 |
awarded | Popular Question |
Aug
17 |
awarded | Yearling |
Oct
3 |
comment |
Most harmful heuristic?
I second, third and fourth that, Darsh. That particular definition of tensor set back my understanding of differential geometry by at least a year. |
Sep
25 |
comment |
Total energy of the Universe
@Willie: Yes, I am aware that quantum gravity is not solved. But I got intrigued when Sean Carroll mentioned the "zero energy" result the Cosmic Variance blog, giving the impression that it was an established consequences of classical general relativity. Learning the actual physics is definitely on the cards - but so much to do, so little time... |
Sep
25 |
accepted | Wiener process related counterexample |
Sep
25 |
comment |
Wiener process related counterexample
Hello Byron and Reda, thanks for replying. Just one thing which is confusing me a little. Reda says, "Byron exhibited another version by changing the process on a set of measure zero". Intuitively, what I understand of Byron's construction is that every path is being broken "at a different point in time". Thus, all the paths are discontinuous, but the joint distributions of the random variables W(t) remain unchanged. Is that what you mean as well ? |
Sep
25 |
asked | Wiener process related counterexample |
Sep
16 |
comment |
Borel Sets on $\mathbb{R}^n$
Ok, done. Proved Step 1, with the standard trick of: - Consider all sets of the form A1 x R^(n-1) which belong to Borel sets of R^n, where A1 is a set in R - Showed that was a sigma algebra - Since (a, b) x R^(n-1) is in Borel sets of R^n, A1 can any Borel set of R. Thanks for the help and the addendum. |
Sep
15 |
accepted | Borel Sets on $\mathbb{R}^n$ |
Sep
15 |
comment |
Borel Sets on $\mathbb{R}^n$
No, this wasn't a homework problem. I've been wondering whether B(R^n) should be defined as the smallest sigma algebra containing all rectangles, or the smallest sigma algebra containing all products of Borel sets in R. I was trying to prove that these are equivalent, and getting worried that I couldn't and I was getting stuck trying to do step 1 as you suggested. Ok, just need to try harder then... |
Sep
15 |
asked | Borel Sets on $\mathbb{R}^n$ |
Sep
14 |
accepted | Total energy of the Universe |
Sep
14 |
comment |
Total energy of the Universe
Curiouser and curiouser ! The claim that the total energy of the Universe is zero is usually used to make the grander claim that "hence, the Universe could spontaneously arise from Nothing without violating conservation of energy". But Shing-Yau result suggests that the zero energy claim and its corollary is nonsense !! Thanks. Let me post this on some physics blogs and see what they have to say. |
Sep
14 |
comment |
Total energy of the Universe
I've been searching the astronomy and physics blogs, but they all seem to state the result without further backup. Plus, the conditions under which this holds are nowhere clarified. It made me think this may be a question for mathematical physicists. |