by Alex Appel 151 days ago | link | parent I don’t believe that $$x_{:n}^{!k}$$ was defined anywhere, but we “use the definition” in the proof of Lemma 1. As far as I can tell, it’s a set of (j,y) pairs, where j is the index of a hypothesis, and y is an infinite history string, rather like the set $$h^{!k}$$. How do the definitions of $$h^{!k}$$ and $$x^{!k}_{:n}$$ differ?

 by Vadim Kosoy 151 days ago | link 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? reply

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