Let (X,M,mu) be a measure and let phi: X to [0,infinity] be M
measurable. Define nu(E):= integral over E phi dmu for E belongs to M.

  verify the followng statements:

 1) nu is a measure on M.
 2) If F is M- measurable and non-negative then integral fdnu=
integral fphidmu.
 3) Let F be any M-measurable function(extended real or complex
valued). Then f is nu - integrable if and only if f phi is
mu-integrable. If so the formula in b) holds again.


   Here PHI is called a DENSITY of nu with respect to mu.

 nu is called the measure with mu-density phi.