On the convergence and law of large numbers for the non-Euclidean L^p-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 L²-means: Let the Lp-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 Lp-mean estimator equals the mean of the distributions of the random variables; and (ii) the limit N ∞ of the Lp-mean estimator also equals the mean of the distributions.