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- Title
Some remarks on the moment problem and its relation to the theory of extrapolation of spaces.
- Authors
Lykov, K.
- Abstract
It is well known that that the coincidence of integer moments ( nth-power moments, where n is an integer) of two nonnegative random variables does not imply the coincidence of their distributions. Moreover, we show that, given coinciding integer moments, the ratio of half-integer moments may tend to infinity arbitrarily fast. Also, in this paper, we give a new proof of uniqueness in the continuous moment problem and show that, in that problem, it is impossible to replace the condition of coincidence of all moments by a two-sided inequality between them, while preserving the inequality between the distributions. In conclusion, we study the relationship with the theory of extrapolation of spaces.
- Subjects
EXTRAPOLATION; ORLICZ spaces; DISTRIBUTION (Probability theory); MEASURE theory; MOMENT problems (Mathematics)
- Publication
Mathematical Notes, 2012, Vol 91, Issue 1/2, p69
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434612010087