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--- math105-s22:notes:lecture_5 [2022/02/01 07:39]
pzhou
+++ math105-s22:notes:lecture_5 [2026/02/21 14:41] (current)
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 ====== Lecture 5 ======
 $\gdef\mcal{\mathcal{M}}$
+[[https://berkeley.zoom.us/rec/share/xjmorYXsD5aEU3_mS6oHTOc413MzXAOIKlj5v1LUWOksJVeNeLzhp-QSVBff_AEF.sRwBxAiQgwZnO3D9 | video ]]
 Welcome back to in-person instruction. I will continue type in here as a way to prepare for class.
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 ===== Pugh 6.4: Regularity =====
-Our goal here is to prove that, any Lebesgue measurable set is a Borel set plus or minus a null-set. More precisely. $E$ is Lebesgue measurable, if and only if there is a $G_\delta$-set (countable intersection of open) $G$, and an $F_\sigma$-set, $F$, where $F \In E \In G$, such that $m(G) = m(F)$.
+Our goal here is to prove that, any Lebesgue measurable set is a Borel set plus or minus a null-set. More precisely. $E$ is Lebesgue measurable, if and only if there is a $G_\delta$-set (countable intersection of open) $G$, and an $F_\sigma$-set, $F$, where $F \In E \In G$, such that $m(G \RM F) = 0$ (why not asking $m(G) = m(F)$? )

Lecture Notes