[see also: beyond, away, off]

The family of 4-sets will be used to generate a symmetry outside $N$ but in $M$.

Outside the fixed points, the group $T$ acts freely on $M$.

In the latter case we may simply adjust $F$ to equal 1 on the Borel set where it falls outside the specified interval.

In the present paper we move outside the random walk case and treat time-inhomogeneous convolutions.

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