This is a note on R. Kaufman’s paper An exceptional set for Hausdorff dimension

We construct a set with and with s.t. for all directions , (the projection of in direction is less than )

, let be an rapidly increasing sequence of integers.

Define

i.e.

Let

rapidly increasing,

Let be fixed, define positive integer sequence s.t.

, we have:

Let where

42.054805
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This entry was posted on October 23, 2009 at 2:20 am and is filed under Uncategorized.

Tags: ergodic, fractal, Furstenberg, Hausdorff dimension, Kakeya

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