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Although it is often intuited as a distance metric, the KL divergence is not a true metric, as the Kullback-Leibler divergence is not symmetric, nor does it satisfy the triangle inequality.
Divergence is a vector operator that measures the magnitude of a vector fields source or sink at a given point.
english?
"Convergence in probability" is a technical term in relation to a series of random variables. Not clear whether this was your question though, I suggest providing more context.
The region of convergence (ROC) of x(z) is the set of all values of z for which x(z) attains a finite value.