Jarník–Besicovitch theorem

E637306

mathematical theorem theorem in metric number theory

The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.

Try in SPARQL Jump to: Statements Referenced by

Statements (35)

Predicate	Object
instanceOf	mathematical theorem ⓘ theorem in metric number theory ⓘ
appliesTo	real numbers ⓘ subsets of the real line ⓘ
area	fractal geometry ⓘ number theory ⓘ
characterizes	Hausdorff dimension of very well approximable numbers ⓘ size of exceptional sets in Diophantine approximation ⓘ
concerns	Hausdorff dimension NERFINISHED ⓘ rational approximation of real numbers ⓘ sets of real numbers ⓘ very well approximable real numbers ⓘ
field	Diophantine approximation NERFINISHED ⓘ metric number theory ⓘ
hasConsequence	precise dimension formula for very well approximable sets ⓘ
hasImportance	fundamental result in metric number theory ⓘ
implies	sets of very well approximable numbers have Lebesgue measure zero ⓘ
isAbout	quantitative size of sets defined by Diophantine inequalities ⓘ
isUsedIn	analysis of approximation properties of typical real numbers ⓘ study of fractal sets in number theory ⓘ
mathematicalDomain	analysis ⓘ geometric measure theory ⓘ measure theory ⓘ
namedAfter	Abram Samoilovitch Besicovitch NERFINISHED ⓘ Vojtěch Jarník NERFINISHED ⓘ
refines	Khintchine-type results in Diophantine approximation ⓘ
relatedTo	Hausdorff dimension theory ⓘ Jarník theorem NERFINISHED ⓘ Khintchine theorem NERFINISHED ⓘ sets of badly approximable numbers ⓘ
topic	distribution of well-approximable numbers ⓘ metric properties of Diophantine approximation ⓘ
usesConcept	Hausdorff measure NERFINISHED ⓘ approximation exponent ⓘ limsup sets ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Diophantine approximation → hasKeyResult → Jarník–Besicovitch theorem ⓘ