Proposition 6 D2 Consider two distributions F( and G( with the same mean. Then the following statements are equivalent (1)F( second-order stochastically dominates G( 2) G( is a mean preserving spread of F() If G(is a mean preserving spread of F(, then ∫a(x)dG(x)=∫(∫a(x+=)lH1(=)lp(x)≤ Lud(x+a)dHx()dF(x)=u(dF(x)Proposition 6.D.2 Consider two distributions F(.) and G(.) with the same mean. Then the following statements are equivalent: (1) F(.) second-order stochastically dominates G(.). (2) G(.) is a mean preserving spread of F(.). If G(.) is a mean preserving spread of F(.), then  uxdGx   x  z ux  zdHxzdFx   x u z x  zdHxzdFx   uxdFx