TY  - BOOK
AU  - Simon,Barry
TI  - Convexity : an analytic view point
T2  - Cambridge tracts in mathematics
SN  - 9781107007314 
U1  - 516.08 
PY  - 2011///
CY  - Cambridge, UK, New York
PB  - Cambridge University Press
KW  - Convex domains
KW  - Mathematical analysis
N2  - "Convexity of sets and functions are extremely simple notions to define, so it may be somewhat surprising the depth and breadth of ideas that these notions give rise to. It turns out that convexity is central to a vast number of applied areas, including Statistical Mechanics, Thermodynamics, Mathematical Economics, and Statistics,and that many inequalities, including Hl̲der's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hl̲der, Minkowski, and Jensen), the Hahn-Banach theorem as a statement about extending tangents to convex functions, and the introduction of two constructions that will play major roles later in this book: the Minkowski gauge of a convex set and the Legendre transform of a function"--
ER  -