=+2P n, then prove that = Q and = Q. Furthermore, prove that strict inequality

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=+2P n, then prove that π = πQ and μ = μQ. Furthermore, prove that strict inequality holds in the inequality

π − μTV = 1 2



i



l

(πl − μl)qli

1 2



l

|πl − μl|



i qli

= π − μTV.

This contradiction gives the desired conclusion. Observe that the proof does not use the full force of irreducibility. The argument is valid for a chain with transient states provided they all can reach the designated state i.)

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