Students should understand the topics outlined in the minimal learning outcomes on the Math 541 Wiki page. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.

Lebesgue measure on Rⁿ

Lebesgue integration on Rⁿ

Fubini's Theorem for Rⁿ

L¹, L², and L^∞

Fourier transform on Rⁿ