On the Differentiation of Henstock and McShane Integrals
It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhe...
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| Main Authors: | , , |
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| Format: | text |
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Archīum Ateneo
2021
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/165 https://www.worldscientific.com/doi/epdf/10.1142/S2591722621400019 |
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| Institution: | Ateneo De Manila University |
| Summary: | It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhere" is a set of points; more precisely; the derivative does not exist on a set of points with measure zero. We can transform a set of Henstock point-interval pairs to a set of points with measure zero because of Vitali's covering theorem. For one-dimensional McShane integrals; n-dimensional McShane and Henstock integrals; covering theorems of the Vitali type cannot be applied. In this paper; we shall discuss differentiation of n-dimensional McShane and Henstock integrals." |
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