Thomas E.
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 May 30 suggested approved edit on $\sigma$-algebras of $\{1,2,3\}$ May 29 answered $\sigma$-algebras of $\{1,2,3\}$ May 29 comment $\sigma$-algebras of $\{1,2,3\}$ The given example is actually closed under complements; so this is not where it fails to be a $\sigma$-algebra. May 29 revised Compactness properties imply continuity deleted 4 characters in body May 29 comment Compactness properties imply continuity Thanks @MTurgeon, I updated my answer:) May 29 revised Compactness properties imply continuity added 1405 characters in body May 25 comment Prove that $f_n$ converges to $f$ in $L_1$ norm given $\int f_n \to \int f$ Sure, didn't know that. Thanks. May 25 revised Prove that $f_n$ converges to $f$ in $L_1$ norm given $\int f_n \to \int f$ added 41 characters in body May 25 answered Prove that $f_n$ converges to $f$ in $L_1$ norm given $\int f_n \to \int f$ May 25 comment Measurability of a simple Set-Valued Map Do you mean that a set-valued map is measurable if preimage of the singleton $S^{-1}(\{O\})$ is measurable for all open sets $O$? Because $S$ is set-valued, then $O$ is an element of its co-domain not a subset, and as far as I'm concerned we don't know a priori that $S$ would be a bijection. Also, what does $\bar{\mathbb{B}}$ represent? May 25 comment Limit points of sets The set of limit points for $B$ is not $\{x^{2}+y^{2}=1\}$: that's its boundary. The set of limit points is $\{x^{2}+y^{2}\geq 1\}$. May 24 comment Integration from 0 to 0 - why does my calculator say “undefined” in one case, and “0” in another? The one-point set $\{0\}$ over which you are integrating is zero measurable: so any measurable function should yield $0$ when integrating over it. However, neither of these functions are defined at $0$, so I think the answer should be "undefined" for both integrals. May 24 answered Limit points of sets May 24 comment Question about proving something using reverse Fatou's lemma @DavideGiraudo: I assumed that $\epsilon$ is the collection of measurable functions, as it is the only reasonable explanation that I could think of. Considering, that this requirement is one of the two assumptions in the Fatou's lemma, other which is stated right after the first verse. May 24 revised Question about proving something using reverse Fatou's lemma added 240 characters in body May 24 revised Question about proving something using reverse Fatou's lemma added 240 characters in body May 24 revised Question about proving something using reverse Fatou's lemma added 6 characters in body May 24 answered Question about proving something using reverse Fatou's lemma May 24 revised neighborhood and topological space Added LaTeX. May 24 suggested approved edit on neighborhood and topological space