12 questions linked to/from Examples of Baire class 2 functions
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### “Representative” Topics in Analysis

I have a lot of time on my hands and want to work on learning some higher level topic in analysis, but one that helps me stay in touch with (and get better) at "standard" topics in analysis. What are ...
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### What is an interval contiguous to the Cantor set?

I have been reading the answer to Examples of Baire class 2 functions , and I'm trying to see what is an example of an interval contiguous to the Cantor set. Could someone lend me a hand?
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### What are examples of real-valued functions of Baire class at least 3?

It's quite easy to find functions of Baire classes 0 and 1; however, the regularity of these functions falls off quite quickly, and with it, ease of construction. The most famous example of a Baire ...
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### Is a function with a dense set of points of continuity of Baire Class 1?

Let $f:[0,1]\to\mathbb R$ be an arbitrary function. It is well known that if $f$ is of Baire Class 1, then the points at which $f$ is continuous form a dense subset of $[0,1]$. My question now is, if ...
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### Examples of functions that do not belong to any Baire class

Recently I read this post, which gives examples of Baire class 2 functions. I have also been reading the Wikipedia article on Baire functions. The article claims that "Henri Lebesgue proved that ... ...
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### Maximum Baire class of a Riemann integrable function

In this answer (see example 1), Andrés Caicedo gives an example of a function $f : [0,1] \to \mathbb{R}$ which is Riemann integrable and is (strictly) of second Baire class. Are there Riemann ...
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### Is the zero set of the Conway base 13 function Borel?

Let $Z$ be the zero set and $S$ the set of numbers that can be written using only the digits 0 through 9 (base 13), which has measure zero. Then $Z^c\subset\mathbb{Q}+S$, which has measure zero.
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