Definition:Strong Pareto Efficiency

Definition
Let $N$ be a finite set.

Let $X \subseteq \R^N$ be a set.

Then $x \in X$ is strongly Pareto efficient there exists no $y \in X$ for which $x_i \le y_i$ for all $i \in N$ and for which $x_i < y_i$ for at least one $i \in N$.