Ash Robert B. Real Variables. 2007

This is a text for a first course in real variables. The subject matter is
fundamental for more advanced mathematical work, specifically in the
areas of complex variables, measure theory, differential equations,
functional analysis, and probability. In addition, many students of
engineering, physics, and economics find that they need to know real
analysis in order to cope with the professional literature in their fields.
Standard mathematical writing, with its emphasis on formalism and
abstraction, tends to create barriers to learning and focus on minor
technical details at the expense of intuition. On the other hand, a certain
amount of abstraction is unavoidable if one is to give a sound and
coherent presentation. This book attempts to strike a balance that will
reach the widest audience possible without sacrificing precision.