# Should I do measure theory ?

Hi All, I am a new phd student in engineering, working in signals analysis in neuroscience who seems to be doing a lot of work in statistics and probability theory. My uni is offering a course in measure theory. The course profile says:

"The course is an introduction to measure theory and Lebesgue integral. A sound knowledge of measure theory and the Lebesgue integral is a starting point to undertake advanced studies in partial differential equations, nonlinear analysis, the calculus of variations and probability theory."

The outcomes of the course are stated as:

"1 Appreciate the central role of sigma-algebras and measure in integration theory;
2 Work with measurable functions and understand their importance to the definition of the integral;
3 Work with the properties of the Lebesgue integral;
4 Generate measures including Stieltjes measures;
5 Use the relationship between the Riemann and Lebesgue integrals on the real line;
6 Understand the relationship between of functions of bounded variation and absolute continuity and the role they play in fundamental theorem of integral calculus;
7 Decompose measures and appreciate the role this decomposition plays in the Radon-Nikodym & Riesz representation theorems;
8 Gain a working knowledge of function spaces and modes of convergence;
9 Work with the integral on product spaces using the relationship with repeated integrals;
10 Apply results from integration theory to other areas of mathematics."

Given that I am not a pure mathematician would it be worth doing this course?

It is always good to know something about functional analysis, measure theory and probability if you want to do theoretical work in signal. But can you survive without knowing any of these? I think you absolutely could. You probably could learn a lot about signal, system, estimation etc without knowing a lot of real analysis. But of course, there are some more theoretical/mathematical topics you would find confusing without those knowledge. I still remember the nightmare when I took a class that I was supposed to learn H-2/H-infinity with very little background. Needless to say it was a total disaster. So, it definitely would help if you know functional analysis.
But before you register for the class, you would definitely need to have taken the undergrad real analysis courses.

What's the prerequisite of this course? It sounds like you need at least undergraduate real analysis course (at the level of Rudin's PMA or equivalent), as chingkui suggested.

Landau