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by Alex Appel 235 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 235 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?

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