Browsing by Subject "CAPACITIES"

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  • Mattila, Pertti (2017)
    Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n and let 0 <u <dim A + dim B n where dim denotes Hausdorff dimension. Let E be the set of those orthogonal transformations g is an element of O(n) for which dim A boolean AND (g(B) + z) n + 1, then dim E 2n-1, then dim A boolean AND (B + z) > u for z in a set of positive Lebesgue measure. If dim A + dim B <2n 1, the set of exceptional g is an element of 0(n) has dimension at most n(n-1)/2-u.
  • Mattila, Pertti (2022)
    For S-g(x, y) = x-g(y), x, y is an element of R-n, g is an element of O(n), we investigate the Lebesgue measure and Hausdorff dimension of Sg(A) given the dimension of A, both for general Borel subsets of R-2n and for product sets.
  • Mattila, Pertti (2021)
    We give conditions on a general family P-lambda : R-n -> R-m, lambda is an element of Lambda of orthogonal projections which guarantee that the Hausdorff dimension formula dim A boolean AND P-lambda(-1){u} = s - m holds generically for measurable sets A subset of R-n with positive and finite s-dimensional Hausdorff measure, s > m, and with positive lower density. As an application we prove for measurable sets A, B subset of R-n with positive s- and t-dimensional measures, and with positive lower density that if s + (n - 1)t/n > n, then dim A boolean AND (g(B) + z) = s + t - n for almost all rotations g and for positively many z is an element of R-n.
  • Ochieng, Robert M.; Arts, Bas; Brockhaus, Maria; Visseren-Hamakers, Ingrid J. (2018)
    Reducing emissions from deforestation and forest degradation in developing countries (REDD+) has opened up a new global discussion on forest monitoring and carbon accounting in developing countries. We analyze and compare the extent to which the concept of measurement, reporting, and verification (MRV) for REDD+ has become institutionalized in terms of new policy discourses, actors, resources, and rules in Indonesia, Peru, and Tanzania. To do so, we draw on discursive institutionalism and the policy arrangement approach. A qualitative scale that distinguishes between "shallow" institutionalization on the one end, and "deep" institutionalization on the other, is developed to structure the analysis and comparison. Results show that in all countries MRV has become institutionalized in new or revised aims, scope, and strategies for forest monitoring, and development of new agencies and mobilization of new actors and resources. New legislations to anchor forest monitoring in law and procedures to institutionalize the roles of the various agencies are being developed. Nevertheless, the extent to which MRV has been institutionalized varies across countries, with Indonesia experiencing "deep" institutionalization, Peru "shallow-intermediate" institutionalization, and Tanzania "intermediate-deep" institutionalization. We explore possible reasons for and consequences of differences in extent of institutionalization of MRV across countries.