nonmeasurable set
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2009 ◽  
Vol 116 (10) ◽  
pp. 926-928 ◽  
Author(s):  
Alexander E. Holroyd ◽  
Terry Soo
Keyword(s):  

2008 ◽  
Vol 45 (3) ◽  
pp. 433-442
Author(s):  
Alexander Kharazishvili ◽  
Aleks Kirtadze

It is shown that, under Martin’s Axiom, the algebraic sum of two universal measure zero subsets of the real line can be an absolutely nonmeasurable set. Some related questions concerning measurability of algebraic sums of small sets are also discussed.


2008 ◽  
Vol 15 (2) ◽  
pp. 317-325
Author(s):  
Alexander Kharazishvili

Abstract We consider some properties of sets and functions which are measurable (or nonmeasurable) with respect to certain classes of measures. In this context, the notion of an absolutely nonmeasurable set (function) is examined. Sierpiński-Zygmund type functions are constructed having additional properties closely connected with the above-mentioned notion. Also, some small subsets of uncountable commutative groups are discussed whose algebraic sum turns out to be an absolutely nonmeasurable set.


2004 ◽  
Vol 11 (3) ◽  
pp. 479-487
Author(s):  
A. Kharazishvili

Abstract The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.


2003 ◽  
Vol 76 (2) ◽  
pp. 137-140
Author(s):  
Saleem Watson ◽  
Arthur Wayman
Keyword(s):  

2003 ◽  
Vol 76 (2) ◽  
pp. 137
Author(s):  
Saleem Watson ◽  
Arthur Wayman
Keyword(s):  

2002 ◽  
Vol 127 (1) ◽  
pp. 41-48
Author(s):  
Mirko Sardella ◽  
Guido Ziliotti
Keyword(s):  

1991 ◽  
Vol 139 (1) ◽  
pp. 17-22
Author(s):  
Marc Frantz
Keyword(s):  

1991 ◽  
Vol 17 (2) ◽  
pp. 781 ◽  
Author(s):  
Balcerzak
Keyword(s):  

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