Infra-Exercises, Part 1

1Charlie Steiner

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pg 6 "there exist" -> "there exists"

pg 13 maybe specify that you mean a linear functional that *cannot* be written as an integral (I quickly jumped ahead after thinking of one where you don't need to take any integrals to evaluate it)

There have been a few remarks about how my and Vanessa’s posts on Infra-Bayesianism seem interesting, but that it's quite a formidable body of work to chew through.

So anyone interested in learning Inframeasure theory to the level of proficiency where they are actually able to develop their own proofs about it and casually deploy it as a tool on other problems is probably not best served by the existing posts. You can only go so far by reading about something without ever applying it.

And so, to help people get a taste for the underlying math, I have constructed a sheet of exercises analogous to Scott's exercise sheets about fixpoints, to guide the reader through inventing most of the basic theory for themselves.

Said problem sheet was dramatically improved by Jack Parker, Connall Garrod, and Thomas Larsen as part of a SERI project, by including proof sketches, relevant definitions, and commentary, and generally making the whole exercise sheet dramatically more polished than it would otherwise be. Several others also contributed to testing out the exercises and providing solutions and feedback, most prominently, Viktoria Malyasova.

This first sheet focuses on introducing Inframeasures, and working through the Fundamental Theorem of Inframeasures. Admittedly, this is a bit distant from much of the later work (further problem sheets are upcoming), but it

isa very important result to have a solid understanding of.There is more information on how to approach the problems in the introduction of the document. We may potentially release more problem sheets in the future, depending on what the feedback to this one looks like. And if the polished versions are not created, I will publish the unpolished ones.

The link to the problems is right here.