A great many results in analysis deal with the question of whether certain properties of sets in \(\mathbb{R}^n\) can be determined by considering only subspaces of lower dimension. For example, Stein showed that a set of positive measure in \(\mathbb{R}^n\), where \(n\ge 3\) must reflect this property to the surface of a sphere. This was shown later for \(n=2\) by Bourgain and Marstrand. In a similar spirit, Fremlin asked the following: Letting \(\lambda\) be Haar measure on the classical Cantor set \(\mathcal{C}\) and supposing that \(\lambda((A+x)∩\mathcal{C})=0\) for all reals \(x\), does it follow that \(A\) is Lebesgue null? I will discuss a result obtained with Marton Elekes on the category analogue of this question.
Reflecting non-meagreness
31.03.2011 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25