Foundations of measure theory?

Click For Summary
SUMMARY

Measure theory is a branch of real analysis that focuses on the concept of measurable sets and the properties of measures, which are non-negative functions defined on collections of subsets. A measure must adhere to specific rules, including countable additivity. Understanding measure theory requires a solid foundation in basic set theory, limits, sequences, series, continuity, and convergence, typically covered in a year-long undergraduate real analysis course. Recommended introductory texts include "Measure Theory" by Alan Weir and "Fundamentals of Measure Theory" by Frank Jones.

PREREQUISITES
  • Basic set theory
  • Limits and continuity
  • Sequences and series
  • Convergence concepts
NEXT STEPS
  • Study "Measure Theory" by Alan Weir
  • Read "Fundamentals of Measure Theory" by Frank Jones
  • Explore countable additivity in measures
  • Review real analysis topics in depth
USEFUL FOR

Students and professionals in mathematics, particularly those pursuing advanced studies in real analysis and anyone interested in the foundational aspects of measure theory.

tgt
Messages
519
Reaction score
2
What theory are they?

Set theory comes to mind but is that too broad?
 
Physics news on Phys.org
Your question is somewhat vague. However, measure theory starts with the notion of collections of subsets, of a measurable set, which are closed under countable unions and countable intersections. A measure is then defined as a non-negative function of these subsets, which must follow certain rules. Essentially it has to be countably additive.
 
Measure theory is a fairly advanced subject, and it falls under the heading of real analysis. You need to be comfortable with basic set theory (as in all math), limits, sequences, series, continuity, convergence, and other topics that you would see in a year long sequence in undergraduate real analysis. Do you have a more specific question?

Here are two good books to start with if you are starting to learn the subject.

https://www.amazon.com/dp/0521097517/?tag=pfamazon01-20 by Alan Weir

https://www.amazon.com/dp/0763717088/?tag=pfamazon01-20 by Frank Jones
 
Last edited by a moderator:

Similar threads

Undergrad Are slices of measurable functions measurable?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Parallel rectangles contained in oblique rectangle
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Information theory via knot theory
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Norm of integral less than or equal to integral of norm of function
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Measure with respect to complete measure is also complete
  • · Replies 3 ·
Replies
3
Views
2K
MHB Reference request - Measure theory
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Applications of analysis in signal processing/machine learning?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Basic measurement theory question
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad On theorem 1.19 in Folland's and completion of measure
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Connection between absolute continuity of function and measure
  • · Replies 2 ·
Replies
2
Views
3K