On the Convergence and Law of Large Numbers for the Non-Euclidean Lp-Means

This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean L-p-means, known to be true for the Euclidean L-2-means: Let the L-p-mean estimator, which constitutes the specific functional that estimates the L-p-mean of N independent and identically distributed random variables; then, (i) the expectation value of the L-p-mean estimator equals the mean of the distributions of the random variables; and (ii) the limit N -> infinity of the L-p-mean estimator also equals the mean of the distributions.