About: Anderson's theorem

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In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function f over an n-dimensional convex body K does not decrease if K is translated inwards towards the origin. This is a natural statement, since the graph of f can be thought of as a hill with a single peak over the origin; however, for n ≥ 2, the proof is not entirely obvious, as there may be points x of the body K where the value f(x) is larger than at the corresponding translate of x.

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rdf:type	yago:WikicatTheoremsInGeometry yago:WikicatTheoremsInRealAnalysis yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293 yago:WikicatProbabilityTheorems
rdfs:label	Anderson's theorem (en)
rdfs:comment	In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function f over an n-dimensional convex body K does not decrease if K is translated inwards towards the origin. This is a natural statement, since the graph of f can be thought of as a hill with a single peak over the origin; however, for n ≥ 2, the proof is not entirely obvious, as there may be points x of the body K where the value f(x) is larger than at the corresponding translate of x. (en)
dcterms:subject	Probability theorems Theorems in geometry Theorems in real analysis
Wikipage page ID	10614125 (xsd:integer)
Wikipage revision ID	1017825267 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability space Probability theorems Real analysis Convex set Mathematics Geometry Convex body Level set Symmetry Theorems in geometry Euclidean space Graph of a function Probability density function Probability theory Random variable Theodore Wilbur Anderson Theorems in real analysis Dimension Integral Negative number
sameAs	Anderson's theorem Anderson's theorem Anderson's theorem Anderson's theorem
dbp:wikiPageUsesTemplate	dbt:About dbt:Cite_journal dbt:Short_description
has abstract	In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function f over an n-dimensional convex body K does not decrease if K is translated inwards towards the origin. This is a natural statement, since the graph of f can be thought of as a hill with a single peak over the origin; however, for n ≥ 2, the proof is not entirely obvious, as there may be points x of the body K where the value f(x) is larger than at the corresponding translate of x. Anderson's theorem also has an interesting application to probability theory. (en)
gold:hypernym	Result
prov:wasDerivedFrom	wikipedia-en:Anderson's_theorem?oldid=1017825267&ns=0
page length (characters) of wiki page	3460 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Anderson's_theorem
is Link from a Wikipage to another Wikipage of	List of probability topics List of real analysis topics Geometric measure theory Catalog of articles in probability theory List of theorems Globally integrable function
is Wikipage redirect of	Globally integrable function
is foaf:primaryTopic of	wikipedia-en:Anderson's_theorem

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