According to Anselin, a LISA statistic have to satisfy two requirements:

a) The LISA for each observation gives an indicator of the extent of significant spatial clustering of similar values around that observation.

b) The sum of LISAs for all observations is proportional to a global indicator of spatial association.

The second requirement is very straightforward but I cannot understand mathematically the first requirement.

For example, he said in his paper "The L_i should be such that it is possible to infer the statistical significance of the patter of spatial association at location i. More formally, this requires the operationalization of a statement such as Prob[L_i>δ_i]≤α_i..." Is this the first requirement?