Vol. 31, No. 1, 1969

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ISSN: 0030-8730
On the inversion formula for the characteristic function

T. Kawata

Vol. 31 (1969), No. 1, 81–85
Abstract

In the inversion formula

                  1-∫ T e−ixt −-1
F (x )− F(0) = Tli→m∞ 2π − T − it  f(t)dt

for the characteristic function f(t) of a distribution function F(x), the limit of the symmetric integral is used. The purpose of this paper is to give a necessary and sufficient condition for the existence of the asymmetric improper integral limT,T′→∞ TT on the right of the above formula.

Mathematical Subject Classification
Primary: 60.20
Milestones
Received: 20 November 1968
Published: 1 October 1969
Authors
T. Kawata