Riemann Integral Construction Of A Sequence Of Functions In A Normed Space (l^p,‖∙‖_p )
DOI:
https://doi.org/10.20956/jmsk.v16i3.8314Keywords:
Normed space l^p, Riemann integral construction, Sequence of functionsAbstract
We construct Riemann Integral for a sequence in a normed space (l^p,‖∙‖_p ). To do construction, we used some theories of real analysis and functional analysis, include some real sequences theories, some Riemann integral theory for functions in R, and some norm theories in a normed space (l^p,‖∙‖_p ). In this paper, we otained that a sequence of functions f=(f_k ):[a,b]⊂R→l^p qualify that the sequence is Riemann integrable on [a,b]⊂R.References
Aji, P. (2016). Integral Riemann Bernilai Barisan l^1. Skripsi. Bandar Lampung: Universitas Lampung.
Bartle, R. G., & Sherbert, D. R. (2011). Introduction to Real Analysis, 4th Edition. United States of America: John Wiley & Sons, Inc.
Chernysh, E. (2018). The Riemann Integral For Functions Mapping To Banach Spaces. Departmen of Mathematics, McGill University.
Kreyzig, E. (1978). Introductory Functional Analysis with Application. Canada: John Wiley & Sons, Inc.
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