MHB Reference request - Measure theory

[Joppy]

Hi!

Can anyone recommend a good introductory book for measure theory? I've found Terence Tao's online book to be a good start, but would I be asking too much if I wanted something even more introductory?

Ultimately I'm working toward Ergodic theory (and probability theory along the way) with an applied focus if that helps.

Thanks.

 

[Math Amateur]

Hi!

Can anyone recommend a good introductory book for measure theory? I've found Terence Tao's online book to be a good start, but would I be asking too much if I wanted something even more introductory?

Ultimately I'm working toward Ergodic theory (and probability theory along the way) with an applied focus if that helps.

Thanks.

You may find Chapters 2-5 of the following book relevant and helpful ...

"Lebesgue Integration on Euclidean Space" by Frank Jones (Revised Edition) Jones and Bartlett Publishers, 2001

Peter

 

[Joppy]

You may find Chapters 2-5 of the following book relevant and helpful ...

"Lebesgue Integration on Euclidean Space" by Frank Jones (Revised Edition) Jones and Bartlett Publishers, 2001

Peter

Thanks Peter! Having a look now.

 

[S.G. Janssens]

Ultimately I'm working toward Ergodic theory (and probability theory along the way) with an applied focus if that helps.

A somewhat unusual book recommended to me once by one of my bosses is Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics by A. Lasota and M.C. Mackey. I am usually a bit allergic for terms such as "chaos" and "fractals", but in this case they should not be deterrents.

The book is not about measure theory itself, but rather it develops those aspects of measure theory that are needed to understand the more "applied" stochastic aspects of various classes of deterministic dynamical systems. It does so in a rigorous but very accessible way, assuming just a good foundation in multivariable calculus. I enjoyed it a lot.

 

[Joppy]

I am usually a bit allergic for terms such as "chaos" and "fractals", but in this case they should not be deterrents.

That's the good stuff isn't it! :p.

The book is not about measure theory itself, but rather it develops those aspects of measure theory that are needed to understand the more "applied" stochastic aspects of various classes of deterministic dynamical systems. It does so in a rigorous but very accessible way, assuming just a good foundation in multivariable calculus. I enjoyed it a lot.

Sounds great, just the sort of thing I was thinking of.

 

[Joppy]

You may find Chapters 2-5 of the following book relevant and helpful ...

"Lebesgue Integration on Euclidean Space" by Frank Jones (Revised Edition) Jones and Bartlett Publishers, 2001

Peter

Honestly I think this is the first mathematical text I've read were I feel as though the author really makes an attempt to explain the reasoning and motivation. Thanks again.

 

[Math Amateur]

Honestly I think this is the first mathematical text I've read were I feel as though the author really makes an attempt to explain the reasoning and motivation. Thanks again.

Joppy,

I have just come across another possibility for you ...

"A User-Friendly Introduction to Lebesgue Measure and Integration" by Gail S. Nelson (AMS 2015)
Yet another book, but more on the Lebesgue integral than Lebesgue measure (although chapter 4 is on measure theory) is the following:

"The Lebesgue Integral for Undergraduates" by William Johnston (MAA Press, 2015)Hope that helps in some way ...

Peter

 

[Joppy]

Joppy,

I have just come across another possibility for you ...

"A User-Friendly Introduction to Lebesgue Measure and Integration" by Gail S. Nelson (AMS 2015)
Yet another book, but more on the Lebesgue integral than Lebesgue measure (although chapter 4 is on measure theory) is the following:

"The Lebesgue Integral for Undergraduates" by William Johnston (MAA Press, 2015)Hope that helps in some way ...

Peter

Great! Thanks a lot.