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arXiv · 2312.00248

On the Riemann integrability of the norm of a path in normed spaces

Borys Álvarez-Samaniego·Wilson P. Álvarez-Samaniego·Luis Rivera
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Abstract

A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in [3]. However, we show that if a bounded path taking values in a normed space is barely Riemann-integrable, then it is not really guaranteed that the norm of this path is also Riemann-integrable.

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Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Luis Rivera. 2023-07-25. On the Riemann integrability of the norm of a path in normed spaces. https://arxiv.org/abs/2312.00248

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