摘要：數(shù)列和函數(shù)的上下極限實(shí)為數(shù)學(xué)分析中的基本概念，其等價(jià)定義也有幾種。本文總結(jié)了數(shù)列上、下極限的5種等價(jià)定義和函數(shù)上、下極限的5種等價(jià)定義，并利用函數(shù)上、下極限的概念來(lái)定義廣義導(dǎo)數(shù)， 將廣義導(dǎo)數(shù)和Clarke意義下的廣義梯度對(duì)比。

關(guān)鍵詞： 上極限; 下極限; 等價(jià)；廣義導(dǎo)數(shù)

Abstract:The sequence and in the function about limit actually mathematical analysis's basic concept, its equal definition also has several kinds and has given the sequence top and bottom limit 5 kinds of equal definitions and the function top and bottom limit 5 kinds of equal definitions, and defines the generalized derivatives using the function top and bottom limit's concept, under generalized derivatives and Clarke significance generalized gradient contrast.

Key words: Top limit; Bottom limit; Equal; Generalized derivatives

　　數(shù)列和函數(shù)的上下極限實(shí)為數(shù)學(xué)分析中的基本概念，其等價(jià)定義也有幾種，往往在學(xué)習(xí)和應(yīng)用的時(shí)候造成混亂，作者希望通過(guò)該課題的研究對(duì)此概念的各種等價(jià)定義進(jìn)行整理，進(jìn)行相關(guān)證明，并利用函數(shù)的上、下極限定義廣義導(dǎo)數(shù)。