Strong consistency of least squares estimate in multiple regression when the error variance is infinite

Let Y-i = x'(i)beta + e(i), 1 less than or equal to i less than or equal to n, S-n = Sigma(i=1)(n) xix'(i). Suppose that the random errors e(1),e(2),. .. are i.i.d., with a common distribution F belonging to the class F-r = {F : integral(-infinity)(infinity) xdF = 0, 0 < integral(-infinity)(infinity) } for some r is an element of [1,2). In this paper ne obtain a sufficient condition for the strong consistency of the Least Sequares Estimate (LSE) < (beta)over cap>(n) of beta. The condition is necessary in the following sen se: If the condition is not satisfied, then for some F is an element of F-r , <(beta)over cap>(n) rails to converge a.s. to beta.