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- Lebesgue_integration abstract "In mathematics, the integral of a non-negative function can be regarded in the simplest case as the area between the graph of that function and the x-axis. Lebesgue integration is a mathematical construction that extends the integral to a larger class of functions; it also extends the domains on which these functions can be defined. It had long been understood that for non-negative functions with a smooth enough graph (such as continuous functions on closed bounded intervals) the area under the curve could be defined as the integral and computed using techniques of approximation of the region by polygons. However, as the need to consider more irregular functions arose (for example, as a result of the limiting processes of mathematical analysis and the mathematical theory of probability) it became clear that more careful approximation techniques would be needed to define a suitable integral. Also, we might wish to integrate on spaces more general than the real line; the Lebesgue integral provides the right abstractions needed to do this important job.The Lebesgue integral plays an important role in the branch of mathematics called real analysis and in many other fields in the mathematical sciences, and is named after Henri Lebesgue (1875–1941) who introduced the integral in (Lebesgue 1904). It is also a pivotal portion of the axiomatic theory of probability.The term "Lebesgue integration" may refer either to the general theory of integration of a function with respect to a general measure, as introduced by Lebesgue, or to the specific case of integration of a function defined on a sub-domain of the real line with respect to Lebesgue measure.".
- Lebesgue_integration thumbnail Integral-area-under-curve.svg?width=300.
- Lebesgue_integration wikiPageExternalLink ksspis.php?wyd=10&jez=pl.
- Lebesgue_integration wikiPageExternalLink kstresc.php?tom=7&wyd=10&jez=pl.
- Lebesgue_integration wikiPageExternalLink index.html.
- Lebesgue_integration wikiPageID "26064288".
- Lebesgue_integration wikiPageRevisionID "606714449".
- Lebesgue_integration hasPhotoCollection Lebesgue_integration.
- Lebesgue_integration id "p/l057860".
- Lebesgue_integration title "Lebesgue integral".
- Lebesgue_integration subject Category:Definitions_of_mathematical_integration.
- Lebesgue_integration subject Category:Measure_theory.
- Lebesgue_integration type Abstraction100002137.
- Lebesgue_integration type Communication100033020.
- Lebesgue_integration type Definition106744396.
- Lebesgue_integration type DefinitionsOfMathematicalIntegration.
- Lebesgue_integration type Explanation106738281.
- Lebesgue_integration type Message106598915.
- Lebesgue_integration type Statement106722453.
- Lebesgue_integration comment "In mathematics, the integral of a non-negative function can be regarded in the simplest case as the area between the graph of that function and the x-axis. Lebesgue integration is a mathematical construction that extends the integral to a larger class of functions; it also extends the domains on which these functions can be defined.".
- Lebesgue_integration label "Całka Lebesgue’a".
- Lebesgue_integration label "Integral de Lebesgue".
- Lebesgue_integration label "Integral de Lebesgue".
- Lebesgue_integration label "Integrale di Lebesgue".
- Lebesgue_integration label "Intégrale de Lebesgue".
- Lebesgue_integration label "Lebesgue integration".
- Lebesgue_integration label "Lebesgue-Integral".
- Lebesgue_integration label "Lebesgue-integraal".
- Lebesgue_integration label "Интеграл Лебега".
- Lebesgue_integration label "ルベーグ積分".
- Lebesgue_integration label "勒貝格積分".
- Lebesgue_integration sameAs Lebesgueův_integrál.
- Lebesgue_integration sameAs Lebesgue-Integral.
- Lebesgue_integration sameAs Integral_de_Lebesgue.
- Lebesgue_integration sameAs Intégrale_de_Lebesgue.
- Lebesgue_integration sameAs Integrale_di_Lebesgue.
- Lebesgue_integration sameAs ルベーグ積分.
- Lebesgue_integration sameAs 르베그_적분.
- Lebesgue_integration sameAs Lebesgue-integraal.
- Lebesgue_integration sameAs Całka_Lebesgue’a.
- Lebesgue_integration sameAs Integral_de_Lebesgue.
- Lebesgue_integration sameAs m.04kp2.
- Lebesgue_integration sameAs Q853831.
- Lebesgue_integration sameAs Q853831.
- Lebesgue_integration sameAs Lebesgue_integration.
- Lebesgue_integration wasDerivedFrom Lebesgue_integration?oldid=606714449.
- Lebesgue_integration depiction Integral-area-under-curve.svg.
- Lebesgue_integration isPrimaryTopicOf Lebesgue_integration.
