This is immediate from 3.2.
We see from (2.3) that ......
From (2.3) we have ......
Then $X$ is the Swiss cheese obtained from the family $D$.
Thus $A$ can be written as a sum of functions built up from $B$, $C$, and $D$.
From now on, $F$ will be fixed.
Consider the family of ordered triples of elements from $F$.
The main difference from the case of finite coding trees is the presence of limits.
Clearly, the contribution from those $r$ with $A(r)>0$ can be neglected.
In Lemma 6.1, the independence of $F$ from $V$ is surprising at first.
The presence here of the direct summand $H$ is simply to prevent $A$ from having disconnected spectrum.
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