摘要
在紧Hausdorff测度空间上建立了Riemann型的积分理论,证明了函数可积的充要条件是该函数几乎处处连续.提出了Riemann积分的可计算性概念,证明了Riemann积分是可计算的当且仅当积分域可以度量化.
The theory of Riemann type integrals is established on compact Hausdorff measure spaces. It is proved that a function is Riemann integrable if and only if it is continuous almost everywhere. The concept of computability of Riemann integrals is proposed and it is proved that Riemann integrals are computable if and only if the spaces are metrizable.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2004年第6期1041-1052,共12页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金重点资助项目(10331010)
