منابع مشابه
Negligible Sets of Radon Measures
Let m be a Radon measure on a Hausdorff topological space X. Corresponding to three kinds of outer measures, three kinds of m-negligible sets are considered. The main theorem states that in a metacompact space X each locally m-negligible set is m-negligible. For a Radon measure in a HausdorfT topological space X we distinguish three kinds of negligible sets corresponding to three kinds of outer...
متن کاملSparsity Regularization for Radon Measures
In this paper we establish a regularization method for Radon measures. Motivated from sparse L regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation detail...
متن کاملMitigation of ineffective measures against radon.
Reasons of low effectiveness of radon remedial measures have been studied on several unsuccessfully remediated houses. Based on the thorough analysis, factors responsible for failures are clarified. The possibilities of how to improve the effectiveness of installed measures are also discussed. Experience in this field is documented by several examples of additionally mitigated houses. After app...
متن کاملLusin type theorems for Radon measures
We add to the literature the following observation. If μ is a singular measure on R which assigns measure zero to every porous set and f : R → R is a Lipschitz function which is non-differentiable μ-a.e., then for every C function g : R → R it holds μ{x ∈ Rn : f(x) = g(x)} = 0. In other words the Lusin type approximation property of Lipschitz functions with C functions does not hold with respec...
متن کاملOn Radon measures on first-countable spaces
It is shown that every Radon measure on a first-countable Hausdorff space is separable provided ω1 is a precaliber of every measurable algebra. As the latter is implied by MA(ω1), the result answers a problem due to D. H. Fremlin. Answering the problem posed by D. H. Fremlin ([4], 32R(c)), we show in this note that, assuming (∗) ω1 is a precaliber of every measurable Boolean algebra, every Rado...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1984
ISSN: 0002-9947
DOI: 10.2307/2000003