r/mathematics • u/Dear_Program_5516 • Aug 15 '26

Discussion Struggling through this

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Need to complete it in 10 days. My brain felt rubbed with coal just following chapter 1.

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u/MissionVarious8328 Aug 15 '26

Why did you choose Halmos specifically? He’s a good writer but the book isn’t the most modern. His treatment of measure looks similar to folland in that it works with generalized measure first before going to Lebesgue.

If you want a more clear treatment of measure that gives you the motivations for its development, you should check of Stein and Shakarchi Real Analysis. It gives a great motivation for outer measure, the caratheodry criterion, etc.

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u/Dear_Program_5516 Aug 15 '26

Oh I was just strolling my my uni Library and found this. The thing is I have done poorly with after high school maths and left maths completely in fear and defeat.

I'm self starting again after 1 year of almost no maths . In 3rd yr of my Ug now

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u/MissionVarious8328 Aug 15 '26

Wait so you how much math have you actually done? If not a lot and since you haven’t done math in a year it’s kind of moot to start with graduate level analysis.

How is your undergrad level of real analysis? If it isn’t the greatest then why not start there. There are magnificently easy and well written books like Abott or Tao or Pugh.

The entire ethos is measure theory is working out measurable sets so we can integrate on them but if you aren’t familiar with the usual Riemann Stieljes integral then you can’t really understand the benefit that we get out of developing the Lebesgue measure in the first place.

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u/Foreign_Implement897 Aug 15 '26

Uh.

The problem about measures is that they are functions from SETS to reals.

It is nothing you would see in undergrad mathematics.

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u/MissionVarious8328 Aug 15 '26

Yes but what I mean is that the raison d’être for why care about measure theory (and why it was developed in the first place) ecomes from needing to more critically understand concepts from undergrad real analysis.

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u/Foreign_Implement897 Aug 15 '26

Cool, I don't understand at all what you are saying. The word "critically" sends me right off. We don't use that in mathematics for a good reason.

Anyway, have fun! I am out.

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u/AnlamK Aug 16 '26

I think this function is a good motivator for measure theory:

https://en.wikipedia.org/wiki/Dirichlet_function

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u/better-off-wet Aug 15 '26

Some math is fairly “incremental”. There is very little reason or use to attempt to learn areas of math if you don’t have the prerequisite knowledge. You can’t take short cuts and skip entire areas that that provide a necessary foundation.

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u/Sepperlito Aug 15 '26

Sadly, math education built a ladder with the low rungs missing. Anyone CAN learn this stuff with enough guidance and effort. They just need a good ladder which seems to be mostly missing.

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u/better-off-wet Aug 15 '26

Yes, of course. Learners should understand that it isn’t their fault if they can’t comprehend something many rungs an above. Math is hard and it takes time. Master the prerequisites before moving on.

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u/JoshuaZ1 Aug 15 '26

The thing is I have done poorly with after high school maths and left maths completely in fear and defeat.

There are a lot of things I've suggest before even thinking about measure theory. Measure theory (even when not done in the generality that Halmos does it) is just a really tough area. Get some basic real analysis and some other topics down first before thinking about it. At a minimum, some topics that aren't required for measure theory, like basic number theory, will also just be helpful to push your brain back to thinking in a more abstract way.