Strong Cesàro summability

Summary

Strong Cesàro summability asks that the partial sums of a series stay close to a value $s$ on average, measured by the mean of $\abs{s_k - s}^q$. Ordinary Cesàro summation only asks that the mean of $s_k - s$ tends to $0$, which allows positive and negative deviations to cancel. For exponent $q \ge 1$, strong Cesàro summability implies Cesàro summability to the same value. It is used in the theory of Fourier series and is closely tied to statistical convergence.