About: Discontinuities of monotone functions

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In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump discontinuities and there are at most countably many of them.

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rdfs:label	Discontinuities of monotone functions (en)
rdfs:comment	In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump discontinuities and there are at most countably many of them. (en)
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Citation dbt:Cite_book dbt:Cite_journal dbt:Efn dbt:Harvtxt dbt:Mvar dbt:Notelist dbt:Reflist dbt:Sfn dbt:Short_description dbt:Use_dmy_dates dbt:Var dbt:Collapse_end dbt:Collapse_begin
Subject	Articles containing proofs Continuous mappings Theorems in real analysis
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Discontinuities_of_monotone_functions?oldid=1071843993&ns=0
Wikipage page ID	22278053 (xsd:integer)
page length (characters) of wiki page	27908 (xsd:nonNegativeInteger)
Wikipage revision ID	1071843993 (xsd:integer)
Link from a Wikipage to another Wikipage	London Mathematical Society Null set Wiley (publisher) Addison-Wesley Alexandru Froda Almost everywhere Monotonic function Sequence Step function Bounded set Cambridge University Press Articles containing proofs Continuous mappings Dini derivative Disjoint sets Jean Gaston Darboux Classification of discontinuities Princeton University Press Springer Science+Business Media Closed set Compact space Countable set Henri Lebesgue One-sided limit Restriction (mathematics) Empty set Indicator function Heine–Borel theorem Injective function Interval (mathematics) Mathematical Association of America Numerical analysis Mathematics Rational number Real-valued function Theorems in real analysis
has abstract	In the mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable; all discontinuities of such a (monotone) function are necessarily jump discontinuities and there are at most countably many of them. Usually, this theorem appears in literature without a name. It is called Froda's theorem in some recent works; in his 1929 dissertation, Alexandru Froda stated that the result was previously well-known and had provided his own elementary proof for the sake of convenience. Prior work on discontinuities had already been discussed in the 1875 memoir of the French mathematician Jean Gaston Darboux. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Discontinuities_of_monotone_functions
is Wikipage redirect of	Froda's theorem
is Link from a Wikipage to another Wikipage of	List of theorems Alexandru Froda Monotonic function Jean Gaston Darboux Classification of discontinuities List of Romanian inventors and discoverers Froda's theorem
is known for of	Alexandru Froda
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Discontinuities_of_monotone_functions

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