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!

Measure Theory

  1. Jul 1, 2009 #1
    Hi, I am pursuing graduate studies in economics, and I hear that "measure theory" is one of the classes that will impress admission commitees. I don't see anything by that name in my school's catalog. Does this class go by another name sometimes?
     
  2. jcsd
  3. Jul 1, 2009 #2
    Yes. Look for a course that covers Lebesgue integration. Some Colleges/Universities offer such a course at the undergraduate level (named something like Second Course in Analysis) or at the graduate level (named something like Introduction to Topology and Analysis).
     
  4. Jul 1, 2009 #3
    Quite a few years ago, I attended a lecture given by John Kenneth Galbraith, and he was asked what he thought of all the advanced math that was coming into Economics. He said he approved, because it would keep the undiligent out of the field.

    Petek is correct. Measure theory is integral calculus on steroids. Lebesgue showed how to integrate over some really weird, but useful things. It has tremendous applications in probability and stats.
     
  5. Jul 2, 2009 #4
    I attended a lecture given by John Kenneth Galbraith, and he was asked what he thought of all the advanced math that was coming into Economics. He said he approved, because it would keep the undiligent out of the field.

    Petek is correct. Measure theory is integral calculus on steroids. Lebesgue showed how to integrate over some really weird, but useful things.
     
  6. Jul 2, 2009 #5

    statdad

    User Avatar
    Homework Helper

    You should realize that in most cases you will need a good footing in mathematics prior to jumping into measure theory. At a bare minimum advanced calculus: a more realistic background would have you with some real analysis and topology.

    I saw measure theory in
    1) A second real analysis course
    2) A measure theory course
    3) Functional analysis
    4) Courses in probability
     
  7. Jul 2, 2009 #6
    Measure theory is used in economics?
     
  8. Jul 2, 2009 #7

    statdad

    User Avatar
    Homework Helper

    I wondered about that too - unless it is for background prep in econometrics, I'm not sure how it would apply.
     
  9. Jul 3, 2009 #8
    Why not? Measure theory is needed to make your MRI scanner work, too. As Wigner pointed out, math is unreasonably effective.
     
  10. Jul 3, 2009 #9

    statdad

    User Avatar
    Homework Helper

    "Measure theory is needed to make your MRI scanner work, too." ?

    The applications of analysis in econometrics are not that theoretical - I would guess that one (or some combination) of the following is true:
    1) the OP is genuinely interested in a broad mathematical background
    2) the "impress entrance committees" comment was thrown out to the OP as a generality - if an applicant has successfully completed mathematics through measure theory he/she has a good background
    3) the comment was made as part of a larger discussion concerning prep for some probability/statistics course(s) that will be required
    4) all of our comments are conjecture, based on nothing more than inadequate information

    whatever the explanation, I hope the OP's endeavors are successful.
     
  11. Jul 4, 2009 #10
    Yep. They rely on the Radon-Nikodym theorem to do their image processing.
     
  12. Jul 4, 2009 #11
    The MRI does not "rely" on any theorem. That's like saying your restaurant bill depends on the inductive hypothesis.
     
  13. Jul 5, 2009 #12

    statdad

    User Avatar
    Homework Helper

    The closest I could find to "dependance" on measure theory is the article summarized here:
    "We present a new medical imaging principle which allows reconstruction of images (from the output of a general digital imaging technology) whose contrast is based on a fundamentally different mathematical mechanism than that of standard images. These images have the useful property that they are capable of exhibiting high contrast between tissues which in currently produced images necessarily have low contrast. The meaning of these images, and their general place in the context of present image generation techniques, is most naturally expressed in the formalism of measure theory. The property actually imaged is derived from a probability measure associated with the mapping which expresses the output of the imaging technology. It also has a nonprobabilistic interpretation as a generalization of the Jacobian, specifically, the Radon-Nikodym derivative. In particular, unlike standard images, contrast is independent of the metric in the space of physical signals that the imaging technology associates with points of the region to be imaged. Images based on this approach using magnetic resonance input are presented."

    Nothing in the article states the process depends (as in would not be possible without) measure theory, but it is an incredibly interesting use of probability and measure theory as an explanatory tool.
     
  14. Jul 5, 2009 #13
    Maybe it would be easiest to tell you directly. What is your school? Then we could look at your school's course offering/catalog to direct you to the right course and/or prerequisites.

    It is most likely offered as a graduate course. I don't think I've seen many schools who offer it as an undergraduate course.
     
  15. Jul 5, 2009 #14
    Most places I've seen (in Canada and some in the U.S) offer it as a split class where the grad students are required to do an extra assignment and presentation. The 'typical' route one would take is Basic Calculus -> Real Analysis -> Metric Space Analysis -> Measure Theory.. though posting your school's website will get you a better answer.
     
  16. Jul 5, 2009 #15
    I can't tell whether you are joking or whether you think being pedantic contributes meaningfully to the discussion.

    (But I think my restaurant bill actually does rely on arithmetic working.)
     
  17. Jul 6, 2009 #16
    So the restaurant bills did not exist before Peano?

    You exaggerate the importance of measure theory in the workings of MRIs. Me calling you out certainly isn't just being "pedantic".
     
  18. Jul 7, 2009 #17
    They were not well grounded before Peano. This is akin to manned flight occuring http://www.etsu.edu/math/gardner/wright-brothers/bernoulli.pdf the discovery that Bernoulli's principle was a fundamental part of wing design (designers beforehand mimicked bird wings and other flying edges). Before Peano's principles, people mimicked the behavior of coins and paper money, without knowing that more fundamental principles applied. Then again, I guess it depends on whether you're a Platonist.
     
    Last edited by a moderator: Apr 24, 2017
  19. Jul 7, 2009 #18
    Ya we're heading into the dangerous and kweeeeeizee world of philosophy. Let's stop.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Measure Theory
  1. Measure of the reals (Replies: 2)

  2. Radian measure (Replies: 1)

  3. Measurement Problem (Replies: 4)

Loading...