Measure Theory and Integration

2010 ◽  
pp. 115-189
Author(s):  
Michael Ruzhansky ◽  
Ville Turunen
Keyword(s):  
Measure Theory

Matrix Completions, Moments, and Sums of Hermitian Squares

2011 ◽  
Author(s):  
Mihály Bakonyi ◽  
Hugo J. Woerdeman
Keyword(s):  
Linear Algebra ◽  
Undergraduate Students ◽  
Complex Analysis ◽  
Measure Theory ◽  
Complex Function ◽  
Complex Function Theory ◽  
Extensive Discussion ◽  
The Subject ◽  
Processing Control ◽  
Developing Area

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.

Measure Theory and Fair Arbiters.

1987 ◽  
Author(s):  
David M. McKeown ◽  
Jr
Keyword(s):  
Measure Theory

scholarly journals Pseudo almost automorphic solutions of class r in α-norm under the light of measure theory

2020 ◽  
Vol 7 (1) ◽  
pp. 81-101
Author(s):  
Issa Zabsonre ◽  
Djendode Mbainadji
Keyword(s):  
Phase Space ◽  
Spectral Decomposition ◽  
Measure Theory ◽  
New Approach ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Automorphic Functions

AbstractUsing the spectral decomposition of the phase space developed in Adimy and co-authors, we present a new approach to study weighted pseudo almost automorphic functions in the α-norm using the measure theory.

The Comprehensive Prediction Model of Rockburst Tendency in Tunnel Based on Optimized Unascertained Measure Theory

2019 ◽  
Vol 37 (4) ◽  
pp. 3399-3411 ◽  
Author(s):  
Qinji Jia ◽  
Li Wu ◽  
Bo Li ◽  
Chunhui Chen ◽  
Yaxiong Peng
Keyword(s):  
Prediction Model ◽  
Measure Theory

scholarly journals Topics of Measure Theory on Infinite Dimensional Spaces

Mathematics ◽  
2017 ◽  
Vol 5 (3) ◽  
pp. 44
Author(s):  
José Velhinho
Keyword(s):  
Measure Theory ◽  
Infinite Dimensional

NUMERICAL APPROACH TO AN OPTIMAL MULTI-ITEM IMPERFECT PRODUCTION CONTROL PROBLEM IN UNCERTAIN ENVIRONMENT

2014 ◽  
Vol 22 (01) ◽  
pp. 125-144
Author(s):  
DIPAK KUMAR JANA ◽  
K. MAITY ◽  
M. MAITI
Keyword(s):  
General Model ◽  
Production Control ◽  
Measure Theory ◽  
Control Variable ◽  
Uncertain Variable ◽  
Production Costs ◽  
Uncertain Measure ◽  
Fuzzy Variables ◽  
Imperfect Production ◽  
Production Inventory

In this paper, some multi-item imperfect production-inventory models without shortages for defective and deteriorating items with uncertain/imprecise holding and production costs and resource constraint have been formulated and solved for optimal production. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. Uncertain or imprecise space constraint is also considered. The uncertain and imprecise holding and production costs are represented by uncertain and fuzzy variables respectively. These are converted to crisp constraint/numbers using uncertain measure theory for uncertain variable and possibility/necessity measure for fuzzy variable. The multi-item production inventory model is formulated as a constrained single objective cost minimization problem with the help of global criteria method. The reduced problem is then solved using Kuhn-Tucker conditions and generalized reduced gradient(GRG-LINGO 10.0) technique. Form the general model, models for particular cases with different production and demand functions are derived. Models for a single item are also presented. The optimum results for different models are presented in both tabular and graphical forms. Sensitivity analysis of average cost for the general model with respect to the changes in holding and production costs are presented.

Maximal linked systems on families of measurable rectangles

2021 ◽  
pp. 77-104
Author(s):  
Aleksandr G. Chentsov
Keyword(s):  
Probability Theory ◽  
Measure Theory ◽  
Cartesian Product ◽  
Wide Sense ◽  
The Family ◽  
Principal Property ◽  
Measurable Structure ◽  
Stone Type ◽  
By Products ◽  
Algebra Of Sets

Linked and maximal linked systems (MLS) on π -systems of measurable (in the wide sense) rectangles are considered (π-system is a family of sets closed with respect to finite intersections). Structures in the form of measurable rectangles are used in measure theory and probability theory and usually lead to semi-algebra of subsets of cartesian product. In the present article, sets-factors are supposed to be equipped with π-systems with “zero” and “unit”. This, in particular, can correspond to a standard measurable structure in the form of semialgebra, algebra, or σ-algebra of sets. In the general case, the family of measurable rectangles itself forms a π -system of set-product (the measurability is identified with belonging to a π - system) which allows to consider MLS on a given π -system (of measurable rectangles). The following principal property is established: for all considered variants of π -system of measurable rectangles, MLS on a product are exhausted by products of MLS on sets-factors. In addition, in the case of infinity product, along with traditional, the “box” variant allowing a natural analogy with the base of box topology is considered. For the case of product of two widely understood measurable spaces, one homeomorphism property concerning equipments by the Stone type topologies is established.

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