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These might be some typos:

From the following, the second $V_{3}$ should be $V_{2}$ :

What can we say about $U$ ? Well, if we fix a $v_{3} \in V_{3}$ , then it will appear in $(\frac{N_{1}}{n_{1}}) (\frac{N_{2}}{n_{2}}) (\frac{N_{3} - 1}{n_{3} - 1})$ of the $U_{σ}$ terms (i.e. all choices of the $V_{1}$ and $V_{3}$ variables, and all possible choices of the other $n_{3} - 1$ variables in the other $N_{3} - 1$ variables in $V_{3}$ ).

as in

(i.e. all choices of the $V_{1}$ and $V_{2}$ variables, and all possible choices of the other $n_{3} - 1$ variables in the other

sj9999

3y00

Generalised models as a category

3y60

I think these might be some typos you could correct:

$Q_{1} (E_{1}) \leq Q_{0} (r^{- 1} (E_{0}))$ , or both measures are undefined.

The $E_{0}$ should be $E_{1}$ .

For such an $r$ -stable set, $Q_{0} (E_{0}) \leq Q_{1} (r (E_{0}))$ and $Q_{1} (r (E_{1}) \leq Q_{0} (r^{- 1} r (E_{0})) = Q_{0} (E_{0})$ , thus $Q_{0} (E_{0}) = Q_{1} (r (E_{0}))$ .

There is a missing parenthesis and the $E_{1}$ should be $E_{0}$ : $Q_{1} (r (E_{0})) \leq Q_{0} (r^{- 1} r (E_{0})) = Q_{0} (E_{0})$

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