The definition of h!k makes sense for anyh, that is, the superscript !k in this context is a mapping from finite histories to sets of pairs as you said. In the line in question we just apply this mapping to x:n where x is a bound variable coming from the expected value.
Hi Alex!
The definition of h!k makes sense for any h, that is, the superscript !k in this context is a mapping from finite histories to sets of pairs as you said. In the line in question we just apply this mapping to x:n where x is a bound variable coming from the expected value.
I hope this helps?