## 8.1. Pointwise Convergence

### Definition 8.1.1: Function Family

A

*family of functions*is defined as a function of two variables*f:*,*x***D****S****R***where the second variable is called***D****R****parameter**. A family of functions is usually written as*{ f*, where the variable_{c}(x) }*x*and the parameter**D***c*. The set**S***is called the domain of the function family, while***D***is the parameter set for the family.***S**