We study the set M ( X ) of full non-atomic Borel measures m on a non-compact locally compact Cantor set X . The set M m = { x ? X : for any compact open set U ? x we have m ( U ) = ∞} is called defective. m is non-defective if m ( M m ) = 0. The set M 0( X ) ì M ( X ) consists of probability and infinite non-defective measures. We classify the measures from M 0( X ) with respect to a homeomorphism. The notions of goodness and the compact open values set S ( m ) are defined. A criterion when two good measures are homeomorphic is given. For a group-like set D and a locally compact zero-dimensional metric space A we find a good non-defective measure m on X such that S ( m ) = D and M m is homeomorphic to A . We give a criterion when a good measure on X can be extended to a good measure on the compactification of X .
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机译：我们研究了非紧局部紧Cantor集X上完全非原子Borel测度m的集合M（X）。集合M m = {x？ X：对于任何紧凑型开放式装置U？ x我们有m（U）=∞}被称为次品。如果m（M m ）= 0，则m是无缺陷的。集合M 0 （X）ìM（X）包含概率和无穷无穷度量。我们根据同胚同质性从M 0 （X）分类度量。定义了善意的概念和紧凑的开放值集S（m）。给出了两个良好的度量是同胚的准则。对于类似群的集合D和局部紧零维度量空间A，我们在X上找到了一个好的无缺陷测度m，使得S（m）= D且M m 同胚于A 。当X的优良度量可以扩展到X的压缩的优良度量时，我们给出了一个判据。
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