Let g and h be real-valued functions defined on R for which «R g(x)dμ and «R h(x)dμ are finite, where μ is a (Ï-finite) measure

Let g and h be real-valued functions defined on R for which ˆ«R g(x)dμ and ˆ«R h(x)dμ are finite, where μ is a (σ-finite) measure in R. Then show that:

In particular, |É›Z| ‰¤ É›|Z|, where Z is a complex-valued r.v.; i.e., Z = X + iY with X and Y real-valued r.v.s.

[g(x) + ih(x)]du < 18(x)+ ih(x)|d.