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This book presents a unified treatise of the theory of measure and
integration. In the setting of a general measure space, every
concept is defined precisely and every theorem is presented with a
clear and complete proof with all the relevant details.
Counter-examples are provided to show that certain conditions in
the hypothesis of a theorem cannot be simply dropped. The
dependence of a theorem on earlier theorems is explicitly indicated
in the proof, not only to facilitate reading but also to delineate
the structure of the theory. The precision and clarity of
presentation make the book an ideal textbook for a graduate course
in real analysis while the wealth of topics treated also make the
book a valuable reference work for mathematicians.
This book is a thorough and self-contained treatise of martingales
as a tool in stochastic analysis, stochastic integrals and
stochastic differential equations. The book is clearly written and
details of proofs are worked out.
This book presents a unified treatise of the theory of measure and
integration. In the setting of a general measure space, every
concept is defined precisely and every theorem is presented with a
clear and complete proof with all the relevant details.
Counter-examples are provided to show that certain conditions in
the hypothesis of a theorem cannot be simply dropped. The
dependence of a theorem on earlier theorems is explicitly indicated
in the proof, not only to facilitate reading but also to delineate
the structure of the theory. The precision and clarity of
presentation make the book an ideal textbook for a graduate course
in real analysis while the wealth of topics treated also make the
book a valuable reference work for mathematicians.The book is also
very helpful to graduate students in statistics and electrical
engineering, two disciplines that apply measure theory.
This volume consists of the proofs of 391 problems in Real
Analysis: Theory of Measure and Integration (3rd Edition).Most of
the problems in Real Analysis are not mere applications of theorems
proved in the book but rather extensions of the proven theorems or
related theorems. Proving these problems tests the depth of
understanding of the theorems in the main text.This volume will be
especially helpful to those who read Real Analysis in self-study
and have no easy access to an instructor or an advisor.
Measure and metric are two fundamental concepts in measuring the
size of a mathematical object. Yet there has been no systematic
investigation of this relation. The book closes this gap.
Measure and metric are two fundamental concepts in measuring the
size of a mathematical object. Yet there has been no systematic
investigation of this relation. The book closes this gap.
This book presents a unified treatise of the theory of measure and
integration. In the setting of a general measure space, every
concept is defined precisely and every theorem is presented with a
clear and complete proof with all the relevant details.
Counter-examples are provided to show that certain conditions in
the hypothesis of a theorem cannot be simply dropped. The
dependence of a theorem on earlier theorems is explicitly indicated
in the proof, not only to facilitate reading but also to delineate
the structure of the theory. The precision and clarity of
presentation make the book an ideal textbook for a graduate course
in real analysis while the wealth of topics treated also make the
book a valuable reference work for mathematicians.The book is also
very helpful to graduate students in statistics and electrical
engineering, two disciplines that apply measure theory.
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