A function is Perron integrable if it has locally small Riemann sums

Journal of the Australian Mathematical Society

Arlo W. Schurle¹ 

关键词: 26 A 39;    26 A 42;   

DOI  :  10.1017/S1446788700033632

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We say that a function has locally small Riemann sums on an interval if for each point x in the interval, and for each positive number ε, all sufficiently fine partitions of intervals lying in neighborhood of x but not containing x have Riemann sums of absolute value less than ε. The main result is then as the title states. We use the generalized Riemann approach to Perron integration, assuming that functions are measurable only to insure that conditions involving the positive and negative parts of the functions are satisfied.

【 授权许可】

Unknown