Inspired by spectral flatness as an application of the inequality between the geometric mean and arithmetic mean, I decided to define something analogous in terms of the Agnesian operator rather than magnitudes from the power spectrum. The Agnesian flatness of order \[k\] for a collection of functions \[S\] parametrized by \[t\] where \[\|S\| = n\] is given by
\[F_{t}^{k}[S] \triangleq\frac{\sqrt[n]{\prod_{j=1}^n \mathcal{A}_t^k [S]}}{\sum_{j=1}^n \mathcal{A}_t^k[\{ x_j(t) \}]}\]
where \(\mathcal{A}_t^k\) denotes the Agnesian as defined in Seilis 2022.