Scholarlink

<p>We introduce various global smallness conditions for Riemann sums within the vector-valued Riemann-measurable function class. In terms of these conditions, we clarify to some extent the nature of the differences between the absolute Birkhoff, McShane and Henstock integrals from one side and the <Emphasis FontCategory="SansSerif">A</Emphasis>-Riemann, <Emphasis FontCategory="SansSerif">A</Emphasis>- and <Emphasis FontCategory="SansSerif">Q</Emphasis>-integrals from the other side. In particular, we prove that the McShane and <Emphasis FontCategory="SansSerif">A</Emphasis>-Riemann integrals do not contradict one another.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On vector-valued functions with small Riemann sums

  • 期刊论文

  • 发表日期：

    2026年3月12日

查看全文
  • K. Naralenkov

摘要

We introduce various global smallness conditions for Riemann sums within the vector-valued Riemann-measurable function class. In terms of these conditions, we clarify to some extent the nature of the differences between the absolute Birkhoff, McShane and Henstock integrals from one side and the A-Riemann, A- and Q-integrals from the other side. In particular, we prove that the McShane and A-Riemann integrals do not contradict one another.