ON THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE MEASURABILITY OF A POSITIVE SEQUENCE
The work is devoted to finding out the necessary and sufficient conditions for the measurability of a sequence of positive numbers. The concept of logarithmic measurability of a sequence is also introduced. It is assumed that the considered sequences form a sequence of zeros of some entire funct...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2019-09-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=6470&lang=en |
| Summary: | The work is devoted to finding out the necessary and
sufficient conditions for the measurability of a sequence of positive
numbers. The concept of logarithmic measurability of a sequence is
also introduced. It is assumed that the considered sequences form
a sequence of zeros of some entire function of exponential type.
Therefore, clarification of this question can be useful in solving the
problem of completeness of the system of exponents or exponential monomials in some convex domain. Such characteristics of the
sequence as lower and upper densities, minimum and maximum
densities, lower and upper logarithmic block densities play an important role. |
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| ISSN: | 2306-3424 2306-3432 |