### S. KANAGAWA1, Y. MOCHIZUKI2 AND H. TANAKA3

1 Department of Mathematics, Yamanashi University, Takeda, Kofu 400, Japan
2 Matsushita Electric Industrial CO. LTD., 1006 Oaza-Kadoma, Kadoma, Osaka 571, Japan
3 Department of Mathematics, Faculty of Science and Technology, Keio University,
Kohoku-ku, Yokohama, Kanagawa 223, Japan

(Received May 1, 1989; revised November 5, 1990)

Abstract.    The limit theorem for the minimum interpoint distance between any pair of i.i.d. random points in Rd with common density f \in L2 was studied by a method which makes use of the convergence of point processes. Some one-dimensional examples with f \notin L2 (including the cases Beta and Gamma distributions) were also considered.

Key words and phrases:    Minimum interpoint distance, Poisson point process, compensator, Skorohod J1-topology.

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