Riemann Integral Construction Of A Sequence Of Functions In A Normed Space (l^p,‖∙‖_p )

Aswad Hariri Mangalaeng,Naimah Aris,Jusmawati Massalesse

doi:10.20956/jmsk.v16i3.8314

Abstract

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.

Highlights

Integrals are one of the important concepts in mathematical analysis that develops very well
Its development began in the late 17th century and to date has been a lot of research that produces the latest theories and the various applications of integrals
Bernhard Riemann discovers that the concept of integrals and derivatives can be separated

Summary

Introduction

Integrals are one of the important concepts in mathematical analysis that develops very well. The integral concept was first put forward by two mathematicians, namely ISAAC Newton in the late 1660s and Gottfried Leibniz in the 1680s. Both found that integrals were the opposite of derivatives. In the concept found by Bernhard Riemann, an integral of a function in the domain in the form of closed and limited intervals , - can be defined without the use of derivatives, which is preceded by partitioning at intervals , - , defining integral value of the function as the limit of Riemann sum. ( is a normed space) and defining the requirements of the function is Riemann integrable on , -.

Riemann Integral Construction

Conclusion