If f is an MT measurble function on Y(extended real-valued or
complex valued) non-negative or muT integrable then foT is
  M measurable and non-negative or mu integrable and we have
 
         integral over Y f dmuT = integral over X foT dmu.

  here MT  and muT are called image sigma algebra and image measure of
M and mu under the mapping t.and  T:X to Y

  and MT is defined as = {B contained in Y/T'(B) belongs to M}

 and muT(B)= mu(T'(B)} for all B belongs to MT.