Joint time scales probability density function

Let $\mathbb{T}$ be a time scale. Let $X$ and $Y$ be random variables. We say that $f_{X,Y}(x,y)$ is a joint time scales probability density function if

1. $f_{X,Y}(x,y) \geq 0$ for all $x,y \in \mathbb{T}$
2. $\displaystyle\int_0^{\infty} \int_0^{\infty} f_{X,Y}(x,y) \Delta y \Delta x=1$.

References

Probability theory on time scales and applications to finance and inequalities by Thomas Matthews