Abstract:One formulation of Marstrand's slicing theorem is the following. Assume that , and is a Borel set with . Then, for almost all directions , almost all of is covered by lines parallel to with . We investigate the prospects of sharpening Marstrand's result in the following sense: in a generic direction , is it true that a strictly less than ‐dimensional part of is covered by the heavy lines , namely those with ? A positive answer for ‐regular sets was previously obtained by the first author. The answer for… Show more
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