| 释义 |
limit superior Given a real sequence (an) which is bounded above, the sequence bn = sup{an, an + 1, an + 2,…} is decreasing and converges to a limit, the limit superior, denoted as limsup an. Similarly if (an) is bounded below, the sequence cn = inf{an, an + 1, an + 2,…} is increasing and converges to a limit, the limit inferior, denoted as liminf an. If bn or cn tends to ±∞, then we define limsup an or liminf an accordingly. Equivalently, limsup an (liminf an) is the greatest (least) limit point of the sequence (an). Note limsup an = liminf an if and only if the sequence an converges (including to ±∞).
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