We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

Using techniques introduced by C. Güntürk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.

Many modern multiobjective evolutionary algorithms (MOEAs) store the points discovered during optimization in an external archive, separate from the main population, as a source of innovation and/or for presentation at the end of a run. Maintaining a bound on the size of the archive may be desirable or necessary for several reasons, but choosing which points to discard and which to keep in the ...

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional

The domain-theoretic model of computational geometry provides us with continuous and computable predicates and binary operations. It can also be used to generalise the theory of computability for real numbers and real functions into geometric objects and geometric operations. A geometric object is computable if it is the effective limit of a sequence of finitary partial objects of the same type...

In this note we investigate propagation of smallness properties for solutions to heat equations. We consider spectral projector estimates the Laplace operator with Dirichlet or Neumann boundary conditions on a Riemanian manifold without boundary. show that using new approach Logunov and Malinnikova (2018) allows one extend type Jerison Lebeau (1999) from localisation open sets localization arbi...