I would like to know if there are any 'accessible' books to understand measure theory. I came across videos of Jay Cummings on YouTube channel 'The Bright Side of Mathematics' (if anyone knows that) and fould almost everything I was looking for, except for the fact that I couldn't truly get through the first videos until sigma algebras are introduced. I cannot picture in my mind any understandable example, what basics I am missing not to be able to understand them? I have been through some abstract algebra but that didn't help, except for the formalism.
$\begingroup$
$\endgroup$
2
-
$\begingroup$ This should be asked on math.stackexchange $\endgroup$– Vladimir DotsenkoCommented Dec 15, 2023 at 12:37
-
$\begingroup$ Surely the most understandable example is a finite set, then the integers, then the real number line, then the plane. After that, I don't know any examples of measure spaces which are different from these in an interesting way, and I don't remember meeting any in a first measure theory course. $\endgroup$– Ben McKayCommented Dec 15, 2023 at 14:21
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Halmos, Paul R. Measure Theory. D. Van Nostrand Co., Inc., New York, 1950. xi+304 pp.
Malliavin, P. Intégration et probabilités. Analyse de Fourier et analyse spectrale, Masson, Paris, 1982. 200 pp.
Kadets, Vladimir A course in functional analysis and measure theory, Universitext. Springer, Cham, 2018.
Tao, Terence An introduction to measure theory. Graduate Studies in Mathematics, 126. American Mathematical Society, Providence, RI, 2011.
answered Dec 15, 2023 at 12:38