On nonatomic submeasures on . II |
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| Authors: | Lech Drewnowski Tomasz &#x;uczak |
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| Institution: | aFaculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland |
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| Abstract: | It is shown that if two submeasures on  that are lim sup's of sequences of measures have the same zero sets, and one is nonatomic, so is the other, and they are (ε-δ)-equivalent. Moreover, if a submeasure η is the lim sup of a sequence of lower semi-continuous (lsc) submeasures and is 0-dominated by the so-called core γ• of an lsc submeasure γ, then η is also (ε-δ)-dominated by γ•. And if a submeasure η of this type is 0-dominated by a nonatomic submeasure, then it is nonatomic as well. |
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| Keywords: |   Submeasure on  sciencedirect " target="_blank">com/cache/MiamiImageURL/B6WK2-4STYV55-5-6/0?wchp=dGLzVtz-zSkzV" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=11 width="13"/> Nonatomic Zero-ideal Analytic ideal Nested partitions |
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