Cantor集及Cantor函数在构造反例中的应用

Cantor集及Cantor函数在构造反例中的应用

摘 要：本文主要介绍Cantor 集和Cantor函数的构造及重要性质,着重讨论了它们在构造反例中的运用。我们还讨论了类Cantor集，即具有正测度的Cantor集的定义、性质及其在构造反例中的应用。

关键词：Cantor集；Cantor函数；可测集。

The Study of cantor set and Cantor function with

Their Applications in constructing Counter Examples

Abstract : In this paper,we discuss measurable the set Cantor set and Cantor function mainly.We construct some

counter examples in Real Analysis by studying their foundamental properties.We also study a class of Cantor sets possessing positive measure and apply these corresponding results to construct some counter examples.

Keywords : Cantor set ;Cantor function; Measurable set.