Can some one tell me what this notation means : N^|| →

Question

M stands for a mechanism and N is for all possible natural numbers. I cannot figure out is X the size of the data set or not ?

Answer 1

First: $|X|$ is probably the number of elements of $X$, so let's assume that's true and set $k = |X|$. Then $N^{|X|}$ is the set of $k$-tuples of natural numbers

If $M:\Bbb{N}^{|X|}\rightarrow \Bbb{R}$, then $M$ is a function that maps a $k$-tuple of natural numbers into the set of real numbers.