EconPapers    
Economics at your fingertips  
 

Updating Hardy, Littlewood and Pólya with Linear Programming

Larry Shepp ()
Additional contact information
Larry Shepp: Rutgers University

A chapter in The Mathematics of Preference, Choice and Order, 2009, pp 403-420 from Springer

Abstract: Some of the standard inequalities that mathematicians use can be proven with convexity arguments or linear programming.1 Perhaps others cannot, so we might say that an inequality is “simple” if there is a convexity based proof. The Cauchy-Schwarz inequality, which may be the most famous and useful inequality ever found is simple in this sense Steele (2004), but there are so many proofs of it that it seems that almost any method will give one, so it may be that it is simple in any sense. The Schwarz inequality can be stated for a general measure space but it easily reduces to the statement that $$EX^2 EY^2 \ge (EXY)^2 $$ where X and Y are any r.v.'s on a common probability space, Ω.. Equality holds if and only if X and Y are proportional.

Keywords: Probability Measure; Extreme Point; Linear Programming Problem; Rigorous Proof; Optimal Pair (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stcchp:978-3-540-79128-7_25

Ordering information: This item can be ordered from
http://www.springer.com/9783540791287

DOI: 10.1007/978-3-540-79128-7_25

Access Statistics for this chapter

More chapters in Studies in Choice and Welfare from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2025-03-23
Handle: RePEc:spr:stcchp:978-3-540-79128-7_25