Polar sets

Stream: maths

[Moritz Doll]

For arbitrary dualities there are several different definitions of a polar set: (a) the absolute polar (b) the real polar, where the real polar comes in two different flavors: $\mathfrak{R} \langle x, y\rangle \leq 1$ (as in Schäfer for instance) and $\mathfrak{R} \langle x, y\rangle \geq -1$ (as in Bourbaki). Does someone have any strong opinions on which definition to take? I would think Bourbaki is always the obvious choice, but in this case the Bourbaki convention is the one which is seen the least.

[Sebastien Gouezel]

I don't have any informed opinion, but I think the principle of least surprise is relevant: if there is no obvious choice, it is probably a good idea to follow the convention that is most often used in (modern) books or articles.