... compact¹

A locally compact group is always tacitly assumed to be a Hausdorff space.

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... groups²

We assume that $G(\mathbb R)$ is a so-called split form. Without this assumption the formulation is more complicated.

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... ``coupled''³

There is confusion here with the use of the word coupling by probabilists.

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... (Pickard).⁴

These models are also popular in crystallography.

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... vertical⁵

This used to be very realistic, but in modern oil recovery wells can be made at different angles.

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