\[ s(X)<\prod_{i=1}^{k} s(x_{i}), where, x_{i}\in X, s(x_{i})= support of x_{i} \]
\[ \frac{|D_{\alpha }|}{|D_{\beta }|}\geq \tau, 0< \tau \leq 1 \]
where τ is called the core ratio
\[ Dist(\alpha,\beta)=1-\frac{|D_{\alpha }\cap D_{\beta }|}{|D_{\alpha }\cup D_{\beta }|} \]
\[ Dist(\alpha,\beta)\leq 1-\frac{1}{2/\tau -1}=r(\tau) \]
\[ D(P_{1},P_{2})=1-\frac{|T(P_{1})\cap T(P_{2})|}{|T(P_{1})\cup T(P_{2})|}e \]