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 Lp-means, known to be true for the Euclidean L2-means: Let the Lp-mean estimator, which constitutes the specific functional that estimates the Lp-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.