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    C[a,b]-Valued Measure and Some of its Properties

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    F. MIPA_Prosiding_Firdaus Ubaidillah_VALUED MEASURE AND SOME OF ITS PROPERTIES.pdf (1.203Mb)
    Date
    2014-05-18
    Author
    UBAIDILLAH, Firdaus
    DARMAWIJAYA, Soeparna
    INDRATI, Ch. Rini
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    Abstract
    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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    http://repository.unej.ac.id/handle/123456789/101114
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    • LSP-Conference Proceeding [1846]

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