1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Foundations of measure theory?

  1. Apr 4, 2009 #1


    User Avatar

    What theory are they?

    Set theory comes to mind but is that too broad?
  2. jcsd
  3. Apr 4, 2009 #2


    User Avatar
    Science Advisor

    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.
  4. Apr 5, 2009 #3
    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/Lebesgue-Int...sr_1_1?ie=UTF8&s=books&qid=1238983053&sr=8-1" by Alan Weir

    https://www.amazon.com/Lebesgue-Int...sr_1_1?ie=UTF8&s=books&qid=1238983133&sr=1-1" by Frank Jones
    Last edited by a moderator: Apr 24, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook