In the definition of the Perron integral of a function f (x) over a closed interval [a, b] a major function M(x) and a minor function m(x) are required to satisfy the conditions (i) M(x) and m(x) are continuous on [a, b] and M(a) = m(a) = 0 ; (ii) - ∞ ≠ Ḏ M(x) ≥ f (x) ≥ D [overscored] m(x) ≠ + ∞. It is shown that without restricting the generality of the integral one may impose the additional condition (iii) M(x) and m(x) are differentiable on [a, b]. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/41334 |
| Date | January 1951 |
| Creators | McGregor, James Lewin |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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