 supported on <span class="math inline">\(\mathbb{R}_+^P\)</span> and <span class="math inline">\(\mathbb{R}_-^P\)</span> respectively. Thus the largest possible difference is at least the difference between the probabilities that <span class="math inline">\(\mu_+\)</span> and <span class="math inline">\(\mu_-\)</span> assign to the set of positive <span class="math inline">\(P\)</span>-dimensional reals, which is <span class="math inline">\(1\)</span>. Therefore <span class="math inline">\(d_{\text{TV}}(F_