ON ERDOSH ONE PROBLEM FOR EXTENSIONS OFLEBESGUE MEASURES

G. Pantsulaia

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ON ERDOSH ONE PROBLEM FOR EXTENSIONS OFLEBESGUE MEASURES

机译：关于Lebesgue度量扩展的一个Erdosh问题

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A negative answer is given to the question of [2] for extensions of the n-dimensional Lebesgue measure ?_n in R~n (n ≥ 2). More precisely, in the theory ZFC, we construct an extension λ of the ?_n such that for every positive constant c there exists a λ-measurable set E_c for which the λ-measure of E_c is larger than c and the E_c contains no the vertices of a triangle of area one.

机译：对于[2]的问题，否定答案是将n维Lebesgue度量？_n扩展为R〜n（n≥2）。更准确地说，在理论ZFC中，我们构造了？_n的扩展λ，使得对于每个正常数c，都有一个λ可测量的集合E_c，其中E_c的λ度量大于c，并且E_c不包含面积一的三角形的顶点。

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《Hadronic Journal》 |2009年第4期|425-432|共8页
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G. Pantsulaia;
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P.O. Box 0143, 77 Kostava Street Department of Mathematics Georgian Technical University, Tbilisi, Georgia P.O. Box 0142, 2 University Street Institute of Applied Mathematics Tbilisi State University, Tbilisi, Georgia;

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ON ERDOSH ONE PROBLEM FOR EXTENSIONS OFLEBESGUE MEASURES

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