# P-norms for p<1

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I'm interested in thing that are norms except for the fact that they satisfy the reverse triangle inequality $$||x+y|| \geq ||x|| + ||y||$$. The obvious example is taking p-norms for 0<p<1. Does anyone know of others or if there's any theory developed on this topic?

Are you requiring the norm to be positive definite? If so, I'm pretty sure that your space can have only one point.

EDIT: the p norms don't satisfy the reverse triangle inequality: take x = -y.

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