What does Sigma notation mean, in the context of computability of functions? I was reading a paper on the computability of AIXI [1] and came across the notion of $\Sigma^0_n$-computability for real-valued functions in section 2.3. 

I'd like to read about this in more detail.
Unfortunately I couldn't find this definition anywhere else in the literature. I already checked the references given at the end of the paper. 

Could somebody point me to some book/article I can take a look at?




On the Computability of AIXI by J. Leike and M. Hutter (2015)
Section 2.1 of that paper defines such computability for sets of natural numbers, and Section 2.3 of that paper then extends the notion to real-valued functions.