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We then define
:<math> \kappa(\{j\} | i) = K_{ji} = P(j|i), \qquad \forall i \in X, \quad \forall B \in \mathcal B</math>.
Again the transition probability, the stochastic matrix and the Markov kernel are equivalent reformulations.
===Markov kernel defined by a kernel function and a measure ===
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