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- W4229743997 abstract "Let T be a triangle. P be a parallelogram, E be an ellipse, A , B be concentric circles, C , D be concentric dartboard regions, R , S be rectangles of the same orientation, U, V be two finite unions and/or differences of convex regions in the Euclidean plane. Given a function f on [0,∞), let E [/( r ), U , V ] denote the mean value of f ( | u – v |), where | u – v | is the distance between u ∊ U and v ∊ V . Using Borel’s overlap technique, a specific distance weight function and a specific equivalence relation, we obtain formulae expressing E [ f ( r ), U , V ] in terms of triple integrals, expressing E ( r n , U , V ), E [ f ( r ), A , V ] and E [ f ( r ), R , V ] in terms of double integrals, expressing E [ f ( r ), A , B ], E [ f ( r ), R , S ] , E [ f ( r ), T , T ], E [ f ( r ), P , P ], E ( r n , C , D ) and E ( r n , R , V ) in terms of single integrals, and expressing E ( r n , R , S ), E ( r n , P , P ), E ( r n , T , T ), E ( r n , E , E ) in terms of elementary functions, where n is an integer ≧−1. Many other related results are also given." @default.
- W4229743997 created "2022-05-11" @default.
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- W4229743997 date "1985-12-01" @default.
- W4229743997 modified "2023-09-26" @default.
- W4229743997 title "The distance between two random points in plane regions" @default.
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- W4229743997 doi "https://doi.org/10.1017/s0001867800015391" @default.
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