Lecture Notes

User Tools

Site Tools

You are here: Course Notes » Math 105: A second course to real analysis (2022 Spring) » Students Area » Rasmus Pallisgaard
math105-s22:s:rasmuspallisgaard:start

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision 		Previous revision
math105-s22:s:rasmuspallisgaard:start [2022/03/07 18:42]
pallisgaard [Homework] 		math105-s22:s:rasmuspallisgaard:start [2026/02/21 14:41] (current)
Line 41: Line 41:
  
 {{ :math105-s22:s:rasmuspallisgaard:maht105-hw5-rasmus-pallisgaard-2.pdf |Homework 5}} {{ :math105-s22:s:rasmuspallisgaard:maht105-hw5-rasmus-pallisgaard-2.pdf |Homework 5}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:analysis_ii_-_notes_3.pdf |Homework 6}} (There is a mistake in problem 1, b. I'll fix it and update the file.)
  
 **Resume of Lebesque measure theory** **Resume of Lebesque measure theory**
Line 75: Line 77:
 Proving the other direction, if $E$ has measure zero, then there exists a $G_\delta$-set $G\supset E$, The main step is to set up $X(\alpha)=\{x:m(G_x)>\alpha\}$ for each slice $G_x$. One can then finalise the proof using the same disjointizing method on a compact set $K(x)$ contained in $G_x$ with $m(K(x))=m(G_x)$ and a neighbourhood $W(x)$. Proving the other direction, if $E$ has measure zero, then there exists a $G_\delta$-set $G\supset E$, The main step is to set up $X(\alpha)=\{x:m(G_x)>\alpha\}$ for each slice $G_x$. One can then finalise the proof using the same disjointizing method on a compact set $K(x)$ contained in $G_x$ with $m(K(x))=m(G_x)$ and a neighbourhood $W(x)$.
  
 +{{ :math105-s22:s:rasmuspallisgaard:math105-hw5-rasmus-pallisgaard.pdf |Homework 5}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105_hw6_rasmus_pallisgaard.pdf |Homework 6}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105-hw7-rasmus-pallisgaard.pdf |Homework 7}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105_hw8.pdf |Homework 8}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105_hw9.pdf |Homework 9}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105_hw10.pdf |Homework 10}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105_hw11.pdf |Homework 11}}
 +
 +{{ :math105-s22:s:rasmuspallisgaard:math105-hw12-rasmus-pallisgaard.pdf |Homework 12}}
 +
 +====Final Essay====
 +Here is my final essay on lebesque integration and measure theory, and why its needed and relevant in the context of integration.
  
 +{{ :math105-s22:s:rasmuspallisgaard:final_essay.pdf |Why Do We Need Measure Theory?}}
  
math105-s22/s/rasmuspallisgaard/start.1646678570.txt.gz · Last modified: 2026/02/21 14:43 (external edit)

Page Tools

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
CC Attribution-Share Alike 4.0 International Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki