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- Simple_function abstract "In the mathematical field of real analysis, a simple function is a real-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently 'nice' that using them makes mathematical reasoning, theory, and proof easier. For example simple functions attain only a finite number of values. Some authors also require simple functions to be measurable; as used in practice, they invariably are.A basic example of a simple function is the floor function over the half-open interval [1,9), whose only values are {1,2,3,4,5,6,7,8}. A more advanced example is the Dirichlet function over the real line, which takes the value 1 if x is rational and 0 otherwise. (Thus the "simple" of "simple function" has a technical meaning somewhat at odds with common language.) Note also that all step functions are simple.Simple functions are used as a first stage in the development of theories of integration, such as the Lebesgue integral, because it is easy to define integration for a simple function, and also, it is straightforward to approximate more general functions by sequences of simple functions.".
- Simple_function wikiPageID "1890594".
- Simple_function wikiPageLength "4361".
- Simple_function wikiPageOutDegree "27".
- Simple_function wikiPageRevisionID "674782388".
- Simple_function wikiPageWikiLink Category:Measure_theory.
- Simple_function wikiPageWikiLink Category:Real_analysis.
- Simple_function wikiPageWikiLink Category:Types_of_functions.
- Simple_function wikiPageWikiLink Complex_number.
- Simple_function wikiPageWikiLink Floor_and_ceiling_functions.
- Simple_function wikiPageWikiLink Floor_function.
- Simple_function wikiPageWikiLink Indicator_function.
- Simple_function wikiPageWikiLink Integral.
- Simple_function wikiPageWikiLink Lebesgue_integral.
- Simple_function wikiPageWikiLink Lebesgue_integration.
- Simple_function wikiPageWikiLink Linear_combination.
- Simple_function wikiPageWikiLink Mathematics.
- Simple_function wikiPageWikiLink Measurable.
- Simple_function wikiPageWikiLink Measurable_function.
- Simple_function wikiPageWikiLink Measurable_set.
- Simple_function wikiPageWikiLink Measure_(mathematics).
- Simple_function wikiPageWikiLink Pointwise.
- Simple_function wikiPageWikiLink Real_analysis.
- Simple_function wikiPageWikiLink Real_line.
- Simple_function wikiPageWikiLink Real_number.
- Simple_function wikiPageWikiLink Sequence.
- Simple_function wikiPageWikiLink Serge_Lang.
- Simple_function wikiPageWikiLink Sigma-algebra.
- Simple_function wikiPageWikiLink Step_function.
- Simple_function wikiPageWikiLink Walter_Rudin.
- Simple_function wikiPageWikiLinkText "Simple function".
- Simple_function wikiPageWikiLinkText "simple function".
- Simple_function wikiPageWikiLinkText "simple functions ".
- Simple_function wikiPageWikiLinkText "simple".
- Simple_function hasPhotoCollection Simple_function.
- Simple_function wikiPageUsesTemplate Template:Aut.
- Simple_function subject Category:Measure_theory.
- Simple_function subject Category:Real_analysis.
- Simple_function subject Category:Types_of_functions.
- Simple_function hypernym Function.
- Simple_function type ProgrammingLanguage.
- Simple_function type Type.
- Simple_function type Function.
- Simple_function type Type.
- Simple_function comment "In the mathematical field of real analysis, a simple function is a real-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently 'nice' that using them makes mathematical reasoning, theory, and proof easier. For example simple functions attain only a finite number of values.".
- Simple_function label "Simple function".
- Simple_function sameAs Einfache_Funktion.
- Simple_function sameAs Fonction_étagée.
- Simple_function sameAs פונקציה_פשוטה.
- Simple_function sameAs Funzione_semplice.
- Simple_function sameAs 単関数.
- Simple_function sameAs Funkcja_prosta.
- Simple_function sameAs Função_simples.
- Simple_function sameAs m.0642mv.
- Simple_function sameAs Простая_функция.
- Simple_function sameAs Enkel_funktion.
- Simple_function sameAs Проста_функція.
- Simple_function sameAs Q913022.
- Simple_function sameAs Q913022.
- Simple_function sameAs 简单函数.
- Simple_function wasDerivedFrom Simple_function?oldid=674782388.
- Simple_function isPrimaryTopicOf Simple_function.