Two results for monocompact measures.
Two Selection Theorems
Two theorems on measurable sets and sets having the Baire property
Two-valued measure need not be purely -compact
Two-valued measures on -classes
Two-valued states on a concrete logic and the additivity problem
Type-II singularities of two-convex immersed mean curvature flow
We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular...
Typical Dimension of the Graph of Certain Functions.
Typical measurable function in the topology of close approximation.
Typical multifractal box dimensions of measures
We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on . We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.