The well-known multiple integralwhere R_n is the region defined by x₁ ≥ 0, x₂ ≥ 0, …., x_n ≥ 0, x₁ + x₂ + …. + x_n ≤ 1, and where a₀, a₁, …, a_n are positive constants, can be evaluated either in the classical way using the Dirichlet transformation or by the use of the Laplace transform. I. J. Good has considered a more general integral and has proved the following result by induction:—If f₁(t), f₂(t), …, f_n(t) are Lebesgue measurable for 0 ≤ t ≤ 1, m₁, m₂, …., m_n, m_n+1 (= 0) are real numbers, M_r = m₁ + m₂ + … + m_r, x₁, x₂, …, x_n are non-negative variables and X_r = x₁ + x₂ + … + x^r, thenIt does not seem to be possible to establish this relation by employing the Laplace transform, but we show below that it can be obtained using the Mellin transform.