A compact null set containing a differentiability point of every Lipschitz function

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.Comment: 28 pages; minor modifications throughout; Lemma 4.2 is proved for general Banach space rather than for Hilbert spac

Geoinformation technology for spatial inventory of greenhouse gas emissions: electricity and heat generation in Poland

One of the main features of energy production in Poland is high dependence on consumption of coal and lignite, which results in significant emissions of greenhouse gases (GHGs) to the atmosphere. This article presents the geo- information technology and spatial analysis of GHG emissions from fossil fuel burned by power and combined power and heat plants. These plants are considered as emission sources of a point type. As input data, official regional statistics about consumption of fossil fuel for electricity and heat production are used. In addition, main characteristics of power and power/ heat plants are collected from official web-sites. Based on the developed model, numerical experiments have been carried out for the territory of Poland. The results of spatial modeling are presented in the form of thematic maps

On the derivability of Lipschitz functions

We show that given any Borel measure on , every Lipschitz function is -a. e. differentiable with respect to . © 2001 Springer