To prove a theorem that establishes this property, one considers the average of the first n-plus-1 Dirichlet kernels. Normal families are defined in terms of a weakening of this property called “[this property] on compact subsets.” This property of a sequence of Cesàro means that it is guaranteed for continuous periodic functions by a result of Fejér (“FEH-yair”). This property is implied by a weaker one on a set of nearly full measure by (*) Egoroff’s (10[1])theorem. Boundedness and equicontinuity of a sequence implies the existence of a subsequence with this property (10[1]-5[1])by the Arzela–Ascoli (10[1])theorem. The (-5[1])limit of a sequence of continuous functions with this property is necessarily continuous. In this property's definition, the choice of N is dependent on epsilon, (10[1])but is independent of x. (10[1])For 10 points, name this property that is often contrasted with the weaker pointwise convergence. (10[1])■END■ (10[2])