Be able to prove ow this is metric

** 0 1 Example 9.9: Let S denote the measurable, finite a.e. functions on [0,1], and let If g p(f,g) dX 1 + 1 f g| Again, as in Example 9.8, we shall identify members of S that agree almost everywhere. To verify that this is a metric on S is easy except for the triangle inequality. To prove this, note first that the function t/(1+t) is an increasing function. Thus, if h(t) is between f(t) and g(t), then lf (t) h(t) \f(t) g(t)