Halfway points

As a half space moving perpendicularly to its border crosses a given density distribution, it may be stopped when it contains exactly half of the total mass of the distribution. Any point in common with the boundaries of all such stopped half spaces is called a "halfway point" for the dist...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1992-09, Vol.23 (5), p.1332-1341
Main Authors: BEYER, W. A, SWARTZ, B
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Exact sciences and technology
Fluid mechanics
Mathematical analysis
Mathematics
Measure and integration
Sciences and techniques of general use
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Summary:As a half space moving perpendicularly to its border crosses a given density distribution, it may be stopped when it contains exactly half of the total mass of the distribution. Any point in common with the boundaries of all such stopped half spaces is called a "halfway point" for the distribution. One may regard it as a multidimensional extension of the "median" of one-dimensional distributions. A context in which such points arise is discussed, and some characteristics of distributions that have halfway points are considered.
ISSN:0036-1410
1095-7154
DOI:10.1137/0523075