C[a,b]-Valued Measure and Some of its Properties
Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2014, Yogyakarta State University, 18-20 May 2014
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| Main Authors: | , , |
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| Format: | Academic Paper |
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Faculty of Mathematics and Natural Sciences Yogyakarta State University,
2020-10-09T07:21:11Z.
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| Summary: | Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2014, Yogyakarta State University, 18-20 May 2014 Let 𝐶[𝑎, 𝑏] be the set of all real-valued continuous functions defined on a closed interval [𝑎, 𝑏]. It is a commutative Riesz algebra space with unit element 𝑒, where 𝑒(𝑥) = 1 for every 𝑥 ∈ [𝑎, 𝑏]. As in the real numbers system ℝ, we define 𝐶 ̅[𝑎, 𝑏] of the extended of 𝐶[𝑎, 𝑏]. In this paper, we shall generalize the notions of outer measure, measure, measurable sets and measurable functions from 𝐶[𝑎, 𝑏] into 𝐶 ̅[𝑎, 𝑏]. This paper is a part of our study in Henstock-Kurzweil integral of functions define on a closed interval [𝑓, 𝑔] ⊂ 𝐶[𝑎, 𝑏] which values in 𝐶 ̅[𝑎, 𝑏]. |
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| Item Description: | http://repository.unej.ac.id/handle/123456789/101114 kodeprodi1810101#Matematika |