 In fact, the more finely one partitions the outcome space \(O_{k} = \{o_{k1},\ldots ,o_{kv},\ldots ,o_{kw}\}\) into distinct outcomes that differ on likelihood ratio values, the larger EQI  becomes.[15]  This shows that EQI tracks empirical distinctness in a precise way. The importance of the Non-negativity of EQI result for the Likelihood Ratio Convergence Theorem will become clear in a moment.