The representation of 𝑒^{-𝑥𝜆} as a Laplace integral

According to a theorem of Bochner [l, p. 498 ] l the function e*~*\ for any fixed value of X in 0 \(t) is positive almost everywhere and that ƒ." fa(f)dt < °°.For this last integral is the total variation of ot\(t), suitably normalized.Further information concerning \(t) may be derived from some general results of Post.Let 7 be the contour