ABSTRACT

Now we come to the main topic of our study, namely, the functions in the most general context, which behave like the real valued function y = mx of real variable x. Recall the defining property of this function f(x) = mx. For c1, c2 in R, f(c1x1 +c2x2) = c1f(x1)+c2f(x2). The probability of a randomly chosen function T : V → W to have this property is zero (see Exercise 1, Section 4.1).