An Alternative Definition of the Henstock-Kurzweil Integral Using Primitives

Authors

  • Wee Leng Ng Nanyang Technological University
  • Peng Yee Lee Nanyang Technological University

Keywords:

Henstock-Kurzweil integral

Abstract

We introduce the notion of an H-primitive being the limit of a sequence of absolutely continuous functions satisfying certain conditions and use it to formulate an alternative definition of the Henstock-Kurzweil integral on a closed bounded interval. Furthermore, the definition provides a characterisation of the primitive of a Henstock-Kurzweil integrable function.

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Author Biographies

Wee Leng Ng, Nanyang Technological University

Nanyang Technological University,

1, Nanyang Walk,

Singapore 637616,

Singapore

Peng Yee Lee, Nanyang Technological University

Nanyang Technological University,

1, Nanyang Walk,

Singapore 637616,

Singapore

 

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Published

2018-12-31

How to Cite

Ng, W. L. ., & Lee, P. Y. (2018). An Alternative Definition of the Henstock-Kurzweil Integral Using Primitives. New Zealand Journal of Mathematics, 48, 121–128. Retrieved from https://nzjmath.org/index.php/NZJMATH/article/view/31

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Articles