bility distributions <span class="math inline">\(\mu_F\)</span> and <span class="math inline">\(\mu_F'\)</span> can assign to the same event. It ranges between <span class="math inline">\(0\)</span> and <span class="math inline">\(1\)</span>. Now for <span class="math inline">\(\mathcal{S}_+\)</span> and <span class="math inline">\(\mathcal{S}_-\)</span>, the corresponding empirical distributions, denoted by <span class="math inline">\(\mu_+\)</span> and <span class="math inline">\(\mu_-\)</span>, are fully