Henstock-Kurzweil可积函数所有基元的空间P的Banach-Steinhaus定理

Q4 Mathematics New Zealand Journal of Mathematics Pub Date : 2021-01-01 DOI:10.53733/114

Wee Leng Ng

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摘要

本文利用经典的Hahn-Banach定理和Riesz表示定理，证明了具有一致范数的闭有界区间上henstok - kurzweil可积函数的所有基元的空间P上的Banach-Steinhaus定理是如何从Denjoy空间上的Banach-Steinhaus定理推导出来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Banach-Steinhaus Theorem for the Space P of All Primitives of Henstock-Kurzweil Integrable Functions

In this paper, it is shown how the Banach-Steinhaus theorem for the space P of all primitives of Henstock-Kurzweil integrable functions on a closed bounded interval, equipped with the uniform norm, can follow from the Banach-Steinhaus theorem for the Denjoy space by applying the classical Hahn-Banach theorem and Riesz representation theorem.

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