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math105-s22:notes:lecture_2

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math105-s22:notes:lecture_2 [2022/01/19 11:00]
pzhou created 		math105-s22:notes:lecture_2 [2022/01/24 20:36] (current)
pzhou
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 ====== Lecture 2 ====== ====== Lecture 2 ======
 +{{ :math105-s22:notes:note_jan_20_2022_math105_2.pdf | note}}, [[https://berkeley.zoom.us/rec/share/UqunccB0RH4vHe05wsCk9QBAMg2jJsaCYNkmNGkI9uMyTC2jthz_nTxa8bQ2rmej.eMtr71uH4FJDGzGJ | video]]
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 Last time we had the definition of outer measure, and we basically followed Tao-II's presentation. This time, we will go through Lemma 7.2.5 (relatively easy) and Lemma 7.2.6 (about outer measure of a box, a bit hard). Pugh gives a different proof for the outer measure of a box being what it supposed to be, namely the naive volume, and he uses Lebesgue number. I am going to follow Tao's approach, although it is longer.  Last time we had the definition of outer measure, and we basically followed Tao-II's presentation. This time, we will go through Lemma 7.2.5 (relatively easy) and Lemma 7.2.6 (about outer measure of a box, a bit hard). Pugh gives a different proof for the outer measure of a box being what it supposed to be, namely the naive volume, and he uses Lebesgue number. I am going to follow Tao's approach, although it is longer. 
  
math105-s22/notes/lecture_2.1642618833.txt.gz · Last modified: 2022/01/19 11:00 by pzhou

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