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Is lebesgue integral/measure theory critical for MFE admission?

Hi, I'm an undergraduate mathematics student who aims to apply for MFE program in US and UK this year. And this starting semester is going to be my last term in the undergraduate study.
I thought it quite obvious to study the measure theory/lebesgue integral this semester since I heard it is significantly beneficial for rigorous financial mathematics. I also thought it for myself while reading some journals about the stochastic pdes.
The problem is, the class time overlap with the required courses for graduation, which is complex variables, and it seems I have no choice but give up taking the measure theory course since measure theory course is just the optional major courses for graduation.
So I was wondering if, it would be detrimental to the admission decision if I hadn't took this course. According to the admission requirement each MFE websites state, the required mathematical backgrounds only include linear algebra, probability and statistics, calculus. (And only few schools even mention real analysis which refers to Rudin's PMA, not the measure theory or any elaborate studying about Lebesgue Integrals)
Could someone give an idea about this issue? I'm quite nervous because this is something that I never expected.

Thanks in advance.
 
Could someone give an idea about this issue?

You'd be wasting your time taking a full-blown course on Lebesgue integration. In Klebaner's book on stochastic processes there's coverage of different kinds of integration -- Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, and Ito. That's probably all you'll need (maybe more than what you need for the MFE courses). Just make sure you have your Riemann (and preferably Riemann-Stieltjes) integration down pat. On a side note, the complex integral is really a Riemann-Stieltjes integral though most modern texts elide over this.
 
You'd be wasting your time taking a full-blown course on Lebesgue integration. In Klebaner's book on stochastic processes there's coverage of different kinds of integration -- Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, and Ito. That's probably all you'll need (maybe more than what you need for the MFE courses). Just make sure you have your Riemann (and preferably Riemann-Stieltjes) integration down pat. On a side note, the complex integral is really a Riemann-Stieltjes integral though most modern texts elide over this.
We went over it very broadly in sto Calc 1 but by no means did we go very deep into the mathematics. Some measure theory just to understand but nothing crazy.
You don't need to know measure theory, don't worry. Complex variables is fun, kick some ass.
Thnx guys. I'll just focus on the complex variables then.
 
you will not need in fact measure theory if you take a light stochastic course , but if you tackle existence uniqueness problems there you will need a heavy use of measure theory
 
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