I understand what does it mean for a set to be closed under addition or multiplication, i.e. the sum/product of elements in a set, is still in a set.
Now, I am a little bit confuse when it says the distribution (stable distribution) is closed under convolution.
This is what I think it means, Let D be a family of stable distribution. For any $f, g \in D$, then $(f*g) \in D$ where $(f*g)$ is a convolution of $f$ and $g$, defined by $(f*g) = \int_{-inf}^{inf} f(\tau)g(t-\tau) d\tau $.