TY  - BOOK
AU  - Salamon,Dietmar A.
AU  - Salamon,Dietmar A.
TI  - Measure and Integration
T2  - EMS Textbooks in Mathematics (ETB)
SN  - 9783037196595
PY  - 2016///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Real analysis
KW  - bicssc
KW  - Measure and integration
KW  - msc
N1  - Restricted to subscribers
N2  - The book is intended as a companion to a one semester introductory lecture course on measure and integration. After an introduction to abstract measure theory it proceeds to the construction of the Lebesgue measure  and of Borel measures on locally compact Hausdorff spaces, $L^p$ spaces and their dual spaces and elementary Hilbert space theory. Special features include the formulation of the Riesz Representation Theorem in terms of both inner and outer regularity, the proofs of the Marcinkiewicz Interpolation Theorem and the Calderon–Zygmund inequality as applications of Fubini’s theorem and Lebesgue differentiation, the treatment of the generalized Radon–Nikodym theorem due to Fremlin, and the existence proof for Haar measures. Three appendices deal with Urysohn’s Lemma, product topologies, and the inverse function theorem.  The book assumes familiarity with first year analysis and linear algebra. It is suitable for second year undergraduate students of mathematics or anyone desiring an introduction to the concepts of measure and integration
UR  - https://doi.org/10.4171/159
UR  - http://www.ems-ph.org/img/books/salamon_mini.jpg
ER  -