Separation problem for a family of Borel and Baire G-powers of shift measures on R

The separation problem for a family of Borel and Baire G-powers of shift measures on R is studied for an arbitrary infinite additive group G using the technique developed in [Kuipers L., Niederreiter H. Uniform distribution of sequences. – New York etc.: John Wiley & Sons, 1974], [Shiryaev A. N. Probability (in Russian). – Moscow: Nauka, 1980] and [Pantsulaia G. R. Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces. – New York: Nova Sci. Publ., Inc., 2007].Вивчається задача вiдокремлення для сiм’ї борелiвських та берiвських G-степенiв мiр зсуву на R для довiльної нескiнченної адитивної групи G iз використанням пiдходу, розвиненого в роботах [Kuipers L., Niederreiter H. Uniform distribution of sequences. – New York etc.: John Wiley & Sons, 1974], [Ширяев А. Н. Вероятность. – М.: Наука, 1980] та [Pantsulaia G. R. Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces. – New York: Nova Sci. Publ., Inc., 2007]

Linear criteria for hypotheses testing

In the present paper we prove necessary and sufficient conditions for the existence of linear consistent criteria. Keywords: Statistical structure, Linear consistent criteria, Weakly and strongly linear criteri

The consistent criteria of hypotheses

In this paper we define the consistent criteria of hypotheses such as the probability of any kind of errors is zero for given criteria. We prove necessary and sufficient conditions for the existence of such criteria

The Relationship between Earth's Magnetic Field Variations and Solar Activity

This scientific article investigates the intricate connection between Earth's magnetic field variations and solar activity through a comprehensive analysis of empirical data and mathematical models. It employs advanced statistical analytics and hypothesis testing to elucidate the underlying mechanisms driving this phenomenon. By exploring the complex interplay between solar phenomena and Earth's magnetic field, we aim to advance our understanding of the dynamics governing this crucial aspect of our planet's environment

Cantidation for existence of such criteria

В труде доказаны необходимые и достаточные условия о существовании состоятельных критериев проверки гипотез

A consistent criteria for Gaussian Statistical structure

В труде доказаны необходимые и достаточные условия о существовании состоятельныех критериев проверки гипотез для статистических структур Гаусса

Transactions

ალექსი გორგიძის დაბადებიდან 105 წლისთავისადმი მიძღვნილი შრომათა კრებული. Сборник трудов посвященный к 150 летию со дня рождения Алексея Горгидзе. The collection of works devoted to the 105th anniversary of the birth of the Alexi Gorgidz