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Considering the Ripley's K function as used in spatial point-process analysis, or the closely related L function, I am wondering what the limit of the function is as r approaches infinity. I am aware that the function is not well defined as r increases, but I am stuck on how to go about computing this limit, if it exists. My hunch, just based on intuition, is that the function will continue to increase towards infinity. Any input is appreciated. Thank you.

I have provided the equation for the empirical K function below, as it appears in "Spatial Point Patterns: Methodology and Applications with R" by Baddeley, Rubak, and Turner.

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    $\begingroup$ Perhaps you could write the K-function out so we could see what $r$ refers to? $\endgroup$
    – jbowman
    Commented Mar 28 at 23:27

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It indeed diverges to infinity. Imagine an infinite point process with constant intensity. You can then pick one of the points at random and declare this as the origin of your coordinate system. Then the K-function evaluated at r is the number of points of the point process within distance r of you origin point (not counting the origin). Since the process is stationary more points will be included as you increase r.

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