PMATH 450Measure Theory
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 7 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.
Review of Riemann integration. Measure spaces: sigma-algebras, Borel sets, outer measure, Caratheodory condition, Lebesgue-Steiltjes measures, translation invariance and regularity of Lebesgue measure. Measurable functions: simple approximation, Egorov's and Lusin's theorems. Integration: monotone convergence theorem, Fatou's lemma, Lebesgue dominated convergence theorem. Signed measures: Hahn and Jordan decompositions, absolute continuity of measures, Radon-Nikodym theorem. Lp spaces: completeness, separability, Riesz representation theorem.
Prerequisites
- Must have completed the following:
- PMATH351 - Real Analysis (0.50)
Antirequisites
None listed.
Leads to
Fall 2026 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6363 | 37 / 81 | MWF 14:30–15:20 |
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 450.
- Course notes for PMath 450, An introduction to Lebesgue measure and Fourier series. Course notes · math.uwaterloo.ca · from Laurent Marcoux’s site Remove
- notes.html Course notes · math.uwaterloo.ca · from Stephen New’s site Remove
- Course Notes (Incomplete) Course notes · david-duan.me · posted on r/uwaterloo Mar 2022 Remove
Reviewed on UW Flow
83% liked it36% easy93% useful
From 23 ratings and 14 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
i love andu, and measure theory is pretty cool
Aug 2026 · liked itOn UW FlowRemove this
Took it in Spring 2025 with Blake, the first offering that combines the old 450+451. It was still hard but easier than 351:)
Aug 2025 · liked itOn UW FlowRemove this
Really fun course with Marcoux. His lectures are really clear and the course content is very interesting. The tests though are pretty hard lol.
Dec 2024 · liked itOn UW FlowRemove this
With Marcoux, went very fast in lectures and learnt many analysis tools along the way. Content is very technical and dense but very fruitful.
Dec 2024 · liked itOn UW FlowRemove this
I enjoyed almost every part of it.
Dec 2024 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
129 posts and comments in 111 threads mention PMATH 450, May 2012 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.
Fall 2024
Hardness of First year (math) 4 points, 8 comments
“I am a grade 11 student right now and I want to apply to mathematical finance in the future, but the minimum requirement for it is the minimum grade for each course is 70%. …”
u/shitfartpissballs: “it’s really tough man”
u/LoudChannel5796: “real analysis, Lebesgue Integration, measure theory namely pmath 351, pmath450, pmath 451”
Spring 2024
Is doing CS 456, CS 458, 3x bird courses + 20hr/week job difficult? 8 points, 13 comments
“Do you think this is doable for my 3B term? Not sure how difficult CS 456 and CS 458 are, especially if taking them in the same term, so any insight would be appreciated. …”
u/dave7364: “Is doing CS 452, CS 444, CS 488, CS 343, PMATH 450 and a full time job, and a design team (Waterloop btw) doable? (I have a CAV of 94).”
Winter 2024
Interesting pmath/co courses? 3 points, 2 comments
“What are some particularly interesting pmath/co courses? I don’t have space to take many of them, but wish to maximize my utility. One course I know I want to take is pmath 351. Any other suggestions?”
u/Alone_Letterhead2671: “… PMATH Analysis route: PMATH 450, 451, 453 which are pretty popular. Some topics covered are pretty cool like Measure theory covered in more rigorous version. It's also applicable in lots topic like probability theory, analytics NT, operator theory, optimization, etc. …”
u/Stranger_Natural: “Seconding this, but I also wanted to mention that measure theory (pmath 450, 451) and functional analysis (453) gets used in certain pmath (analysis), co (optimization), and stats (stochastic calculus) topics courses (which you can try to take as an undergrad). …”
Fall 2023
Advice for CS major who doesn’t like CS? 30 points, 7 comments
“I’m a 4A CS major who will graduate in 2025 on my current plan, but I haven’t found a job the past two years and throughout this degree I found I don’t even like CS that much. …”
u/Ok_Meeting_2592: “… \- pmath 348: Offered Fall and Winter \- pmath 365: Offered Winter (take it next term!) \- pmath 450: Offered Winter \- 3 more 4xx pmath courses, depending on your interests. All in all, if you started a pmath major right now, you could still graduate on time. …”
Fall 2022
Math Finance PMATH Courses 14 points, 4 comments
u/QUITIG: “PMATH 333, 351, 450, 451 are required for the math finance major, how difficult are these pmath courses and are they useful for a career in finance? …”
STAT 902 Undergraduate? 1 point, 11 comments
“Has anyone ever taken STAT 902 as an undergraduate before? What do the instructor usually ask as a prerequisite for the course? …”
u/vkoj1221: “I havent taken STAT 901 or STAT 902 but I was allowed to take STAT 901 (as an undergrad with PMATH 450 but no STAT 330). I dropped out of the class because it was looking a little bit like PMATH 451 but easier. I imagine that overriding in is instructor dependent.”
Spring 2022
CS students, what courses have you taken each term 9 points, 21 comments
“Inspired by https://www.reddit.com/r/uwaterloo/comments/v3b8nj/can\any\current\mathcs\students\let\me\know\their/ but recognizing that one term is a very narrow view, What courses have you taken each …”
u/Osteospermum: “… 252 Coop 2 MATH 239 I’m in 3A in the fall, going to (hopefully) take CS 341, PMATH 347, PMATH 450, ECON 101, CLAS 251 Realized in 2B that taking every single hard course I can take every term isn’t worth and it led to me dropping a course (CO 255) and doing worse in my other …”
Winter 2022
What is the hardest course you took in waterloo 29 points, 66 comments
u/PPewt: “PMATH 450 with Ken Davidson around 6 years ago iirc. He decided to rush the course into like 1.5-2mo so that he could squeeze a bunch of theoretical DEs stuff at the end.”
Fall 2021
What are your favourite classes at UW 56 points, 87 comments
u/CliffRouge: “CS246E, PMATH450, STAT333”
How were PMath 450 Oral Exams last term? 4 points, 2 comments
u/vkoj1221: “I heard that Blake Madill conducted oral exams/tests last term and I heard similarly for this term. I was wondering what the format was like and to expect (I am not currently enrolled in the class but I am considering it)”
u/Osteospermum: “Was in math 247 with Blake last term, also had oral exams and I'm pretty sure the format / relative difficulty of exams are comparable to pmath 450. Exams were 3 questions and conducted in groups of 2 students. …”
Imagine Calling Yourself An University of "Beyond Ideas" when You Cockblocked Students from Taking Unusual Steps 137 points, 29 comments
“&x200B; https://preview.redd.it/musbbocny3l71.png?width=666&format=png&auto=webp&s=f3ee68db7b83cf57c7bd8d352a3a6b398cb289db”
u/djao: “I'm not riley, but I am the C&O advisor, and I can explain why we would do something like this. In C&O, you do not need advisor approval in order to enrol in a graduate course as an undergrad. …”
u/djao: “… A realistic set of prerequisites for STAT 901 might be "PMATH 450 and PMATH 451". It's pretty rare for a student who's not in 4A to have met these requirements. …”
u/dotuanhiep: “I actually took PMATH 450 already and will be taking 451 in the Fall. I have asked the professor who is teaching the course and he agreed that I have satisfied the prerequisites. Don’t grad schools look at what courses one takes throughout undergrad? …”
u/djao: “… In truth, I would be more impressed by an aspiring probability student who had taken PMATH 450 + 451 than one who had taken PMATH 450 + STAT 901. The former choice indicates a healthy respect for theory and fundamentals. …”
Denied Override into STATs grad course because of not being in 4A? 0 points, 12 comments
“Is there any other STATs advisor that can give override to grad courses other than Riley? He denied my request because I’m not in 4A. I feel like this is a very arbitrary requirement.”
u/heartuary: “Which course?”
[deleted]: “did you take PMATH 351/450/451? That might help your case. Riley cock-blocked me from taking a course that I later got a 90-something% in. He's not the best at his job, bit too anal on details.”
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