 The meaning of positivity here is that a global Lyapunov exponent is positive for almost all points in the specified set \(S\). This definition certainly is directly connected to SD and is one physicists often use to characterize systems as chaotic. Furthermore, it offers practical advantages when it comes to calculations and can often be “straightforwardly” related to experimental data in the sense of examining data sets generated from physical systems for global Lyapunov   exponents.[2] 