On some questions of R. Gordon related to approximate and dyadic Henstock integrals (Q1803984)
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scientific article; zbMATH DE number 222108
| Language | Label | Description | Also known as |
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| English | On some questions of R. Gordon related to approximate and dyadic Henstock integrals |
scientific article; zbMATH DE number 222108 |
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On some questions of R. Gordon related to approximate and dyadic Henstock integrals (English)
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29 June 1993
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The author answers three questions posed by \textit{R. A. Gordon} [Real Anal. Exch. 16, No. 1, 154-168 (1991; Zbl 0723.26005)]. 1. The example constructed by Tolstov in 1939 demonstrates the existence of a function which is ACG but not \(\text{ACG}_ s\). 2. There exists a continuous function which has a dyadic derivative at each point and is not differentiable on an uncountable set. 3. An \(\text{ACG}_ d\) function has a dyadic derivative almost everywhere.
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approximate Henstock integral
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dyadic Henstock integral
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ACG
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dyadic derivative
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