| Popis: |
We show that for every @e>0 there exists an angle @[email protected](@e) between 0 and @p, depending only on @e, with the following two properties: (1) For any continuous probability measure in the plane one can find two lines @?"1 and @?"2, crossing at an angle of (at least) @a, such that the measure of each of the two opposite quadrants of angle @[email protected], determined by @?"1 and @?"2, is at least [email protected] (2) For any set P of n points in general position in the plane one can find two lines @?"1 and @?"2, crossing at an angle of (at least) @a and moreover at a point of P, such that in each of the two opposite quadrants of angle @[email protected], determined by @?"1 and @?"2, there are at least ([email protected])n-4 points of P. |
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