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Let X be a set and let (An)n∈N be a sequence of subsets of X. Show...

Let X be a set and let (An)n∈N be a sequence of subsets of X. Show that: (a) If (An)n∈N is increasing, then liminf An = limsupAn =S∞ n=1 An. (b) If (An)n∈N is decreasing, then liminf An = limsupAn =T∞ n=1 An.

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