He selected them for students who are presently taking or have just finished courses in calculus and linear algebra, or for people who want to review and improve their skill in real analysis, perhaps as a step toward complex analysis, Fourier analysis, or

Lebesgue integration.

He assumes they have no background in

Lebesgue integration, and admits that this limits applications to problems in concrete function spaces, but notes that there are enough such problems to demonstrate results at considerable length.

The next example is intended for those readers who have knowledge about the

Lebesgue integration.

They should also be acquainted with the theory of

Lebesgue integration, which rather gives away the book's secret ingredient.

de La Vallee Poussin on

Lebesgue integration [14, 10, pp.

This overview of recent concepts and findings in large algebraic substructures is for advanced undergraduate and graduate students with background in calculus of real variables,

Lebesgue integration, set theory, linear algebra, general topology, Hilbert/Banach spaces, complex variables, and holomorphic functions.

However, the

Lebesgue integration requires F' to be integrable over [a, b].

introduces

Lebesgue integration by offering straightforward problems that demonstrate regulated and Riemann integrals, Lebesgue measures and integrals, the integral of unbounded functions, classical Fourier series and ergodic transformations.

Specific subjects covered include

Lebesgue integration, curves and surfaces, integration on surfaces, and a wide variety of others.

Williamson presents students, academics, and mathematicians with an introductory text on

Lebesgue integration.