7:57 let me know if I'm wrong but I think this is incorrect. The sigma algebra of M needs to contain M-itself. Not every set which is in M. M as defined is a set which contains two sets, each of which has only one element. M does not even anywhere appear in the indicated sigma -algebra of M. This has to be wrong I feel. Please let me know if I'm incorrect as I just started studying this subject.
The sigma algebra couldn't contain M because M is not an element of the power set of X. M is a subset of the power set of X. So M is a subset of the sigma algebra generated by M, not an element of the sigma algebra generated by M.
Great thanks for your videos. To my mind this yellow color looks too bright on the dark background. Maybe, colors similar to Zenburn or Solarized color themes for text editors would be an interesting option. Solarized theme allows swapping background and foreground colors without of changing the accent colors.
@@brightsideofmathsYou define the minimal sigma algebra as the intersection of all sigma algebras. But there can be an infinite number of sigma algebras. So the intersection could be a weird limit point.
![Measure Theory 3 | What is a measure? [dark version]](http://i.ytimg.com/vi/GHdBo2uKfiM/mqdefault.jpg)
![Measure Theory 3 | What is a measure? [dark version]](/img/tr.png)
![Measure Theory 1 | Sigma Algebras [dark version]](http://i.ytimg.com/vi/FtEmLexUw3Y/mqdefault.jpg)
7:57 let me know if I'm wrong but I think this is incorrect. The sigma algebra of M needs to contain M-itself. Not every set which is in M. M as defined is a set which contains two sets, each of which has only one element. M does not even anywhere appear in the indicated sigma -algebra of M. This has to be wrong I feel. Please let me know if I'm incorrect as I just started studying this subject.
The sigma algebra couldn't contain M because M is not an element of the power set of X. M is a subset of the power set of X. So M is a subset of the sigma algebra generated by M, not an element of the sigma algebra generated by M.
Great thanks for your videos. To my mind this yellow color looks too bright on the dark background. Maybe, colors similar to Zenburn or Solarized color themes for text editors would be an interesting option. Solarized theme allows swapping background and foreground colors without of changing the accent colors.
Thanks! Maybe you can send me a picture how you want it :)
1:57 Did you mean "just form an intersection" instead of "just form a union" or am I missing something?
You are correct! I wanted to say "intersection"
The definition should be "... contains all the members of \mu".
Fantastic content btw.
Which definition?
Definition of a sigma algebra generated by \mu.
@@mahlatsemthetwa9552 \mu does not generate sigma algebras. Maybe you mean "M"?
Apologies, you're correct I meant 'M'.
How do you know the arbitrary intersection is well defined.
What do you mean?
@@brightsideofmathsYou define the minimal sigma algebra as the intersection of all sigma algebras. But there can be an infinite number of sigma algebras. So the intersection could be a weird limit point.
And why should a weird limit point be a problem? @@freddyfozzyfilms2688
@@brightsideofmaths It wouldn’t be a problem. So will a limit set always exist?
Intersections always exist by the axiom schema of specification from set theory. So at this point, nothing to worry about :D@@freddyfozzyfilms2688
Good talk, subtitle english, not access, spanish based, so future we want english subtitles