论文信息 - OF INTEGRAL EQUATIONS

OF INTEGRAL EQUATIONS

We shall show by a probabilistic approach (distribution functions, the moment problem, etc.) that the only functions satisfying this system of equations for fixed a, 0 <a <2, are g(x) = cx, where c is a constant. It will then be seen that this result is a probabilistic analogue of the well known Cauchy functional equation. Also an application of this result to statistics is presented. THEOREM 1. If g(x) satisfies the Cauchy functional equation (2) g(x + y) = g(x) + g(y),

L. A. Goodman

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