Riemann Integral of Functions from R into Rn

Riemann Integral of Functions from R into Rn In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].

[1]  Yasunari Shidama,et al.  Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support , 2010, Formaliz. Math..

[2]  Yasunari Shidama,et al.  Partial Differentiation on Normed Linear Spaces Rn , 2007 .

[3]  Yasunari Shidama,et al.  Completeness of the Real Euclidean Space , 2005 .

[4]  Czeslaw Bylinski.  Functions and Their Basic Properties , 2004 .

[5]  Krzysztof Hryniewiecki,et al.  Basic Properties of Real Numbers , 2004 .

[6]  Edmund Woronowicz.  Relations and Their Basic Properties , 2004 .

[7]  Jarosław Kotowicz,et al.  Convergent Sequences and the Limit of Sequences , 2004 .

[8]  Czeslaw Bylinski.  Functions from a Set to a Set , 2004 .

[9]  Nagano Katsumi Wasaki.  Scalar Multiple of Riemann Definite Integral , 2004 .

[10]  G. Bancerek,et al.  Ordinal Numbers , 2003 .

[11]  Noboru Endou,et al.  The Definition of the Riemann Definite Integral and some Related Lemmas , 2002 .

[12]  Noboru Endou,et al.  Definition of Integrability for Partial Functions from R to R and Integrability for Continuous Functions , 1994 .

[13]  Jan Popio,et al.  Real Normed Space , 1991 .

[14]  Konrad Raczkowski,et al.  Topological Properties of Subsets in Real Numbers 1 , 1990 .

[15]  Edmund Woronowicz.  Relations Defined on Sets , 1990 .

[16]  Agata Darmochwa,et al.  Topological Spaces and Continuous Functions , 1990 .

[17]  Grzegorz Bancerek,et al.  Segments of Natural Numbers and Finite Sequences , 1990 .

[18]  Czesław Bylí.  Finite Sequences and Tuples of Elements of a Non-empty Sets , 1990 .

[19]  Konrad Raczkowski,et al.  Topological Properties of Subsets in Real Numbers , 1990 .

[20]  Czeslaw Bylinski.  Binary Operations Applied to Finite Sequences , 1990 .

[21]  Czeslaw Bylinski.  The Sum and Product of Finite Sequences of Real Numbers , 1990 .

[22]  Jaross Law Kotowicz.  Real Sequences and Basic Operations on Them , 1989 .

[23]  Czesław Bylí.  Partial functions , 1989 .