Archie
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 Sep 24 awarded Autobiographer Jul 2 awarded Curious Apr 21 awarded Popular Question Oct 4 revised Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem added 227 characters in body Oct 3 comment Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem Wow this is a beautiful answer. My complex analysis course skipped this section involving integration along branch cuts. Thank you! Oct 3 accepted Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem Oct 3 revised Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem added 4 characters in body Oct 3 comment Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem I know. But why? Oct 3 asked Dealing with Residues on the Real Axis - (Evaluation of Improper Integrals) Problem May 12 comment Is $f$ necessarily measurable? Can I use the fact that a function $f$ is Lebesgue measurable if and only if $f_{\big| D}$ and $f_{\big| E -D}$ is Lebesgue measurable where $D$ is a measurable subset of a measurable set $E$? Is this sort of what you were trying to do in your response? May 12 comment Is $f$ necessarily measurable? I guess I'm not understanding the definition of a Lebesgue measurable function. I guess I was trying to say that despite the points of discontinuity, the preimage of $f$ will preserve its measurability (i.e. the pre-image of a measurable set is still measurable under $f$). My professor is covering this section tomorrow and I was trying to work ahead. I'll come back to this once that happens. Thanks. May 12 revised Is $f$ necessarily measurable? added 44 characters in body May 12 comment Is $f$ necessarily measurable? However when we define $f(x_i) = y_i$ wouldn't there be cases when this would be undefined since we stated that the $x_i$'s are the points in which $f$ is not continuous? May 12 comment Is $f$ necessarily measurable? I guess I should have stated Lebesgue measurable set $E$ and we working under the standard topology. But thank you for the input. May 12 comment Is $f$ necessarily measurable? I made an edit for (1), am I on the right track? I'm just having issues sketching the details. May 11 revised Is $f$ necessarily measurable? deleted 199 characters in body May 11 comment Is $f$ necessarily measurable? Also, I edited what I have observed for (1), but I'm still not quite there yet. May 11 comment Is $f$ necessarily measurable? Gah, I feel dumb. Thanks May 11 revised Is $f$ necessarily measurable? added 234 characters in body May 11 asked Is $f$ necessarily measurable?