Abstract
If f is convex on the interval I and X is a random variable with finite expectation, then f(E[X]) ≤ E[f(X)] If f is strictly convex, the inequality is strict unless X is a constant with probability 1.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Hardy, Littlewood, and Pólya (1952) is still a good reference for inequalities.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sydsæter, K., Strøm, A., Berck, P. (2010). Inequalities. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-28518-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
Online ISBN: 978-3-540-28518-2
eBook Packages: Business and EconomicsEconomics and Finance (R0)