Functions of a Real Variable - Elementary Theory PDF

Elementary Theory of Analytic Functions of One or … Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more.

The Theory of Functions of a Real Variable (Second Edition) ... properties of the Lebesgue integral, and give an elementary proof of the ergodic theorem. Let f(x)  ...

Theory of Functions of a Real Variable - Dover … Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis.

An elementary consequence is that entire functions, such as z or ez, have ... our analytic function f (z) is not just a complex function of two real variables x and y.

Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series. Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations Theory of Functions of a Real Variable - Dover …