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We investigate the standard deviation [Formula see text] of the variance [Formula see text] of time series [Formula see text] measured over a finite sampling time [Formula see text] focusing on non-ergodic systems where independent "configurations" c get trapped in meta-basins of a generalized phase space. It is thus relevant in which order averages over the configurations c and over time series k of a configuration c are performed. Three variances of [Formula see text] must be distinguished the total variance [Formula see text] and its
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