We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt \\ &\equiv \int^X_0 D(N, b, t) dt, ...

Non-additive measure theory extends the traditional framework of measure and integration by allowing for measures that do not necessarily satisfy the additivity property. This broader perspective has ...