I have seen in a paper to use the fact that convergence in Ceasaro Mean [Ceasaro Mean] (http://en.wikipedia.org/wiki/Ces%C3%A0ro_mean) implies convergence of the original sequence. This is not true in general. So, what additional condition we need to use to make this happen. Then I can check whether that condition is satisfied in the context ?
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Related: http://math.stackexchange.com/questions/321610/convergence-of-sequence-of-averages-the-other-way-arround – Martin Sleziak Jan 02 '15 at 14:11