The function is called the probability mass function of the random variable .

For the probability density function one has .

If , then .

If , , …, is a partition of the sample space, then for any event one has

Two events are mutually exclusive, if

The integral of a scalar field on the parametrized surface

The scalar function is called the potential of the vector field if .

The function has a maximum at , if for any .

The directional derivative of at with respect to the unit vector is

The function is differentiable at if there exists a linear map such that