Falconer's distance set conjecture states that if a compact subset E of Rd (d > 1) has Hausdorff dimension greater than d/2 then its distance set,
D(E):={|x-y|:x,y E},
has positive Lebesgue measure.

In this lecture, we will discuss the recent progress in this conjecture and closely related Fourier extension estimates relative to fractal measures.

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On 17 Feb 2004, 16:28.