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“Truly continuous” is a synonym for “absolutely continuous”?
No. It is explained in the statment (“the latter means…”).
Absolutely continuous is used in the corollary, which restricts to the σ-finite case.
I’m very pleased to see that so much measure theory is being added to the nLab. Thank you Dmitri!
Yes, it’s great that Dmitri is adding content – here on measure theory and elsewhere!
By the way, if you are fond of measure theory on the Lab, please do consider updating the topic cluster list
when you create a new entry, and don’t forget to add the floating topic cluster menu to all the entries on measure theory, by adding this code at the top of each entry:
+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
### Context
#### Measure and probability theory
+-- {: .hide}
[[!include measure theory - contents]]
=--
=--
=--
(If nothing else, this helps Google spread the word about the content you are adding.)
Actually, now that we are at it, I would like to ask if we can split the “measure and probability theory” context into two, namely, measure theory and probability theory. This for a variety of reasons:
What does the community think?
(Also, is this doable without manually editing a lot of pages?)
I agree, and I can add that probability theory studies random variables and their properties such as independence, as opposed to measure spaces.
Previously, one could see a list of backreferences indicating articles linking to the given article.
I can no longer find it.
Re #8, I can see that one would want to distinguish the two areas, but at the moment the context is calling measure theory - contents. This has a ’thermodynamics’ section too. If we’re only limiting contexts to narrowly defined fields, that section would have to go.
Many of the contents pages have entries in neighbouring fields, e.g., combinatorics - contents has a section on graph theory.
I guess it all depends on how people see the function of these contexts. I barely ever use them.
I see there’s a contents of contents page listing contents pages from 2011-08-10, which could be explored (and updated).
What does the community think?
Do what you find useful for yourself and for users of your pages.
More critical than cosmetic issues is always the content itself. If you take care of compiling a nice comprehensive list of contents for measure theory and/or probability theory, then I can lend a hand with fine-tuning the formatting/layout.
Also, is this doable without manually editing a lot of pages?
No. But if you take care of adding the content I can find 8 minutes to take care of such cosmetic issues. I have practice in doing that :-)
Previously, one could see a list of backreferences indicating articles linking to the given article. I can no longer find it.
This functionality was deactivated long ago because it produced a huge worm of terms at the bottom of each page, blindly wrapping around lines. It would of course be useful to have that list of terms be displayed not by default on each page but on demand. If we want that, I guess we have to ask in “Bugs and feature requests.”
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