This is a continuation of the previous exercise. If f is a function on the state space, we say that g is a normal contraction off if   for all x and   for all x and y. As an example, note that if...

This is a continuation of the previous exercise. If f is a function on the state space, we say that g is a normal contraction off if
  for all x and
  for all x and y. As an example, note that if
  then g is a normal contraction off. Prove that if f ∈ D(E), where E is a Dirichlet form and g is a normal contraction off, then for each t > 0,

Chapter 39