Applications of Measure Theory to Statistics

Gogi Rauli Pantsulaia graduated with a degree in Mathematics from the Iv. Javakhishvili Tbilisi State University (Georgia) in 1982, and received his Ph.D. in Mathematics from the Institute of Mathematics of the Ukrainian Academy of Sciences in 1985.  In 2003 he completed his degree of doctor of physics and mathematics at the I. Vekua Institute of Applied Mathematics of the Iv. Javakhishvili Tbilisi State University (Georgia). He is currently a professor at the Department of Mathematics of the Georgian Technical University. He has participated in more than 10 major research projects and is the author of 4 books and more than 75 papers. His current research interests include set theory, measure theory, probability theory and mathematical statistics.

1 Calculation of Improper Integrals by Using Uniformly Distributed Sequences.- 2 Infinite-Dimensional Monte-Carlo Integration.- 3 On structure of all real-valued sequences uniformly distributed in [-1/2;1/2] from the point of view of shyness.- 4 On Moore-Yamasaki-Kharazishvili type measures and the infinite powers of Borel diffused probability measures on R.- 5 On objective and strong objective consistent estimates of unknown parameters for statistical structures in a Polish group admitting an invariant metric.- 6 Why Null Hypothesis is rejected for "almost every" infinite sample by the Hypothesis Testing of a maximal reliability?.