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Real Analysis is based on the real numbers, and it is naturally
involved in practical mathematics. On the other hand, it has taken on
subject matter from set theory, harmonic analysis, integration theory,
probability theory, theory of partial differential equations, etc., and
has provided these areas with important ideas and basic concepts. This
relationship continues even today. This book, contains the basic matter
of “real analysis” and an introduction to “wavelet analysis,” a popular
topic in “applied real analysis.”
Nowadays, students studying real analysis come from different backgrounds
and have diverse objectives. A course in this subject may serve
both undergraduates and graduates, students not only in mathematics
but also in statistics, engineering, etc., and students who are seeking
master’s degrees and those who plan to pursue doctoral degrees in
the sciences. Written with the student in mind, this book is suitable
for students with a minimal background. In particular, this book is
written as a textbook for the course usually called Real Analysis as
presently offered to first or second year graduate students in American
universities with a master’s degree program in mathematics. |