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I think the original writer wanted P to be the particular rectangle, not the given region. As in the example and even in the theory before that, P as the given region doesn't seem correct. |
→Background: clean up - WP:ACCIM rule #6 using AWB |
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| year = 1987}}.</ref> In other words, any range that intersects at least a proportion ε of the elements of ''P'' must also intersect the ''ε''-net ''N''.
For example, suppose ''X'' is the set of points in the two-dimensional plane, ''R'' is the set of closed filled rectangles (products of closed intervals), and ''P'' is the unit square [0, 1] × [0, 1]. Then the set N consisting of the 8 points shown in the adjacent diagram
For any range space with finite [[VC dimension]] ''d'', regardless of the choice of P, there exists an ε-net of ''P'' of size
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