et <span class="math notranslate nohighlight">\(N'\)</span> be the exact number of initial states. Therefore, in theory, to sum over the states one applies <span class="math notranslate nohighlight">\((1/N') \sum_{I'}\)</span>. However in practice <span class="math notranslate nohighlight">\(N'\)</span> is usually very, very large, and the sum must be discretized, <span class="math notranslate nohighlight">\((1/N') \sum_{I'} \rightarrow \sum_I j_I\)</span> and this array contains that jacobian for each stat