Normal subhypergroup

Symbol-free definition
A subhypergroup of a hypergroup is said to be normal if it commutes with every point measure.

Definition with symbols
A subhypergroup $$H$$ of a hypergroup $$K$$ is said to be normal if $$H * x = x * H$$ for every point $$x \in K$$.

Analogy
The notion of normality for subhypergroup is analogous to the subgroup property of normality, when defined/viewed as follows:

A subgroup $$H$$ of a group $$K$$ is termed normal if $$Hx = xH$$ for all elements $$x \in K$$.

Stronger properties

 * Supernormal subhypergroup

Weaker properties

 * Subhypergroup