Izvorni kôd stranice Ahlswede–Daykinova nejednakost

U statističkoj mehanici, '''Ahlswede–Daykinova nejednakost'''<ref>https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/Ahlswede.pdf</ref><ref>{{Cite journal|last=Reuter|first=Klaus|date=1. 6. 1987|title=Note on the Ahlswede-Daykin inequality|url=https://www.sciencedirect.com/science/article/pii/0012365X87901439|journal=Discrete Mathematics|volume=65|issue=2|pages=209–212|doi=10.1016/0012-365X(87)90143-9|issn=0012-365X}}</ref> je nejednakost četiri funkcije<ref>{{Cite web|url=https://encyclopediaofmath.org/wiki/Ahlswede-Daykin_inequality|title=Ahlswede-Daykin inequality - Encyclopedia of Mathematics|website=encyclopediaofmath.org|access-date=14. 9. 2023}}</ref> na konačnoj [[distributivna rešetka|distributivnoj rešeci]].

Ova nejednakost iskazu je ako je ''&fnof;''<sub>''i''</sub>, ''i'' = 1,&nbsp;2,&nbsp;3,&nbsp;4 su pozitivne funkcije na konačnoj distributivnoj rešeci, tako da je

:<math>f_1(x)f_2(y)\le f_3(x\vee y)f_4(x\wedge y)</math>

za sve ''x'', ''y'' u rešeci, tada je

:<math>f_1(X)f_2(Y)\le f_3(X\vee Y)f_4(X\wedge Y)</math>

za sve podskupove ''X'', ''Y'' rešetke, gdje je

:<math>f(X) = \sum_{x\in X}f(x)</math>

i

:<math>X\vee Y = \{x\vee y|x\in X, y\in Y\}</math>
:<math>X\wedge Y = \{x\wedge y|x\in X, y\in Y\}.</math>

Povezana je sa [[FKG nejednakost]]i, te povlači za sobom [[Holleyjeva nejednakost|Holleyjevu]] u [[Fishburn–Sheppova nejednakost|Fishburn–Sheppovu nejednakost]].

== Reference ==
{{Refspisak}}

== Dodatna literatura ==
*{{Citation | last1=Ahlswede | first1=Rudolf | last2=Daykin | first2=David E. | title=An inequality for the weights of two families of sets, their unions and intersections | doi=10.1007/BF00536201 | id={{MathSciNet | id = 0491189}} | year=1978 | journal=Probability Theory and Related Fields | issn=0178-8051 | volume=43 | issue=3 | pages=183–185}}
*{{springer|id=a/a110440|authorlink=Peter Fishburn|first=P.C. |last=Fishburn}}

[[Kategorija:Nejednakosti]]
[[Kategorija:Statistička mehanika]]