C[a,b]-Valued Measure and Some of its Properties
Date
2014-05-18Author
UBAIDILLAH, Firdaus
DARMAWIJAYA, Soeparna
INDRATI, Ch. Rini
Metadata
Show full item recordAbstract
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].
Collections
- LSP-Conference Proceeding [1874]
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