Convergence of
Average Function Transition Matrix

• $n\times n$ sub matrices of N are stochastic
• Thus u₀N for arbitrary u₀ will also be stochastic.
• The product of two stochastic matrices is itself stochastic.
• Thus each of the terms in M₂, M₃, etc. are stochastic, i.e. all their elements are $\le 1$