Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: M. Kintsurashvili, T. Kiria and G. Pantsulaia
Pages: [83] - [103]
Received Date: March 1, 2016; Revised March 15, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121637
The paper contains a brief description of Yamasaki’s remarkable investigation [19] of the relationship between Moore-Yamasaki-Kharazishvili type measures and infinite powers of Borel diffused probability measures on R. More precisely, we give Yamasaki’s proof that no infinite power of the Borel probability measure with a strictly positive density function on R has an equivalent Moore-Yamasaki-Kharazishvili type measure. A certain modification of Yamasaki’s example is used for the construction of such a Moore-Yamasaki-Kharazishvili type measure that is equivalent to the product of a certain infinite family of Borel probability measures with a strictly positive density function on R. By virtue of the properties of equidistributed sequences on the real axis, it is demonstrated that an arbitrary family of infinite powers of Borel diffused probability measures with strictly positive density functions on R is strongly separated and, accordingly, has an infinite-sample well-founded estimator of the unknown distribution function. This extends the main result established in [20].
Moore-Yamasaki-Kharazishvili type measure, product measure, equidistributed sequence of real numbers.
