On Moore–Yamasaki–Kharazishvili Type Measures and the Infinite Powers of Borel Diffused Probability Measures on R

Gogi Pantsulaia ()
Additional contact information
Gogi Pantsulaia: Georgian Technical University, Department of Mathematics

Chapter Chapter 4 in Applications of Measure Theory to Statistics, 2016, pp 57-71 from Springer

Abstract: Abstract This chapter contains a brief description of Yamasaki’s remarkable investigation (1980) of the relationship between Moore–Yamasaki–Kharazishvili type measuresType measure and infinite powers of Borel diffused probability measures on $$\mathbf{R}$$ R . More precisely, there is given 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 measureType measure . A certain modification of Yamasaki’s example is used for the construction of such a Moore–Yamasaki–Kharazishvili type measureType 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 the properties of real-valued sequences equidistributed on the real axis, it is demonstrated that an arbitrary family of infinite powers of Borel diffused probability measuresDiffused probability measure 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 the paper [ZPS].

Keywords: Borel Probability Measure; Linear Manifold; Infinite Product; Euclidean Vector Space; Finite Borel Measure (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-45578-5_4

Ordering information: This item can be ordered from
http://www.springer.com/9783319455785

DOI: 10.1007/978-3-319-45578-5_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().