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 Nov 12 awarded Nice Answer 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.