Equicontinuity and Sensitivity in Mean Forms

In this paper two mean forms of equicontinuity and sensitivity are mainly studied. For the equicontinuity side, it is shown that any topological dynamical system can be embedded into some almost equicontinuous in the mean system. For the sensitivity side, it turns out that the notions of sensitivity in the mean and mean sensitivity are identical in the measure-theoretical setting, though they are different in the topological setting. Moreover, levels of mean multi-variant versions of sensitivity in topological or measure-theoretical sense are completely classified.