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--- math105-s22:notes:lecture_5 [2022/01/31 23:39]
pzhou
+++ math105-s22:notes:lecture_5 [2022/02/01 23:35] (current)
pzhou
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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