显然有 lim sup An={wlw属于无穷多个An}={wn∈N,k≥n,使w∈A) n→0∞ lim inf An={wlw至多不属于有限多个An}={wl日n∈N,k≥n,有w∈A} n-→o0 从而恒有lim infn-→An C lim supn-→An: 若lim infn→oAn=lim supn→ooAn,则称{An}的极限存 在，并用limno An表示，即令limn→oAn=lim infn→oAn= 7/62 lim supn→An: 特别地，若对每个n,有An C An+1(相应地，An An+1),则称{An}为单调增（相应地，单调降）.对单调增或 单调降序列{An},我们分别令A=UnAn或A=∩nAn, 称A为{An}的极限，通常记为An个A或An↓A. GoBack FullScreen Close Quit7/62 kJ Ik J I GoBack FullScreen Close Quit w,k lim sup n→∞ An = {w|w·uðıáAn} = {w|∀n ∈ N, ∃k ≥ n, ¶w ∈ Ak} lim inf n→∞ An = {w|wñıÿ·ukÅıáAn} = {w|∃n ∈ N, ∀k ≥ n, kw ∈ Ak} l ðklim infn→∞ An ⊂ lim supn→∞ An. elim infn→∞ An = lim supn→∞ AnßK° {An}4Å 3ßø^limn→∞ AnL´ß=-limn→∞ An = lim infn→∞ An = lim supn→∞ An. AO/ßeÈzánßkAn ⊂ An+1(ÉA/ßAn ⊃ An+1)ßK°{An}è¸NO(ÉA/߸N¸).ȸNO½ ¸N¸S {An}ß·Ç©O-A = S n An½A = T n Anß °Aè{An}4Åßœ~PèAn ↑ A½An ↓ A