Measure Theory and Applied Math

[glyvin]

I am starting graduate school in applied math in the fall and am trying to decide if measure theory is necessary or important in terms of applied math and if so, what ares of applied math? I have taken two basic real analysis courses through multiple integrals, etc. and would like to focus on PDE's at this point, although I'm quite open to all areas of applied math at this point. The program I'll be in does not require a class on measure theory, but I do have the option to take one if I'd like.

Thank you for your time.

 

[chiro]

Hey glyvin and welcome to the forums.

For stochastic calculus (or analysis), measure theory is important because we deal with measures that deal with random variables and because of the non-constant nature of the measure (unlike what you would find in a Riemann integral).

Financial mathematics as well as some scientific mathematics based on stochastic processes make use of both measure theory and PDE theory to analyze problems for these fields.