Measure Theory (Bogachev)

First Edition
by V. I. Bogachev

V.I. Bogachev, Measure Theory, Springer, 2007. Two volumes.

Volume I covers constructions and extensions of measures, the Lebesgue integral, operations on measures and functions, the spaces \(L^p\) and spaces of measures, and connections between the integral and derivative. Volume II covers measures on topological spaces, weak convergence, transformations of measures and isomorphisms, conditional measures, and ergodic theory.

Solutions to the Volume I exercises live at Solutions to Bogachev’s Measure Theory, Volume 1.