Cauchy Equations in Several Variables

In this chapter, we will show that a real-valued additive function on Rn can be expressed as a sum of n additive functions of one variable. A similar result holds for real-valued logarithmic function on Rn with some appropriate restrictions on the domain. Further, it will be shown that a real-valued multiplicative function on Rn can be expressed as a product of n multiplicative functions of one variable. A similar result also holds for exponential function on Rn.