= Strong lumpability
{title2=$\sum_{j\in C}p_{ij}=\sum_{j\in C}p_{i\prime j}$}
A partition of a <Markov chain> state space is strongly lumpable when, for every target block $C$, the sum $\sum_{j\in C}p_{ij}$ is identical for all source states $i$ in a given source block. These sums define the <transition matrix> of the block-valued <Markov chain>, independently of the initial law. Failure of this condition means the projection is not guaranteed to be a homogeneous Markov chain for every initial law, although special initial laws may still produce a Markov process.
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