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- Rising_sun_lemma abstract "In mathematical analysis, the rising sun lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund lemma. The lemma is stated as follows:Let g(x) be a real-valued continuous function on the interval [a,b], and let E be the set of x ∈ (a,b) such that g(y) > g(x) for some y with x < y < b.Then E is an open set, and can be written as a disjoint union of intervalssuch that g(ak) = g(bk), except possibly if ak = a when g(bk) ≥ g(ak).The colorful name of the lemma comes from imagining the graph of the function g as a mountainous landscape, with the sun shining horizontally from the right. The set E consist of points that are in the shadow.".
- Rising_sun_lemma thumbnail Rising_sun_lemma.svg?width=300.
- Rising_sun_lemma wikiPageExternalLink 10.
- Rising_sun_lemma wikiPageExternalLink home.html.
- Rising_sun_lemma wikiPageID "17695790".
- Rising_sun_lemma wikiPageRevisionID "601452005".
- Rising_sun_lemma hasPhotoCollection Rising_sun_lemma.
- Rising_sun_lemma subject Category:Lemmas.
- Rising_sun_lemma subject Category:Real_analysis.
- Rising_sun_lemma type Abstraction100002137.
- Rising_sun_lemma type Communication100033020.
- Rising_sun_lemma type Lemma106751833.
- Rising_sun_lemma type Lemmas.
- Rising_sun_lemma type Message106598915.
- Rising_sun_lemma type Proposition106750804.
- Rising_sun_lemma type Statement106722453.
- Rising_sun_lemma comment "In mathematical analysis, the rising sun lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund lemma.".
- Rising_sun_lemma label "Lemme du soleil levant".
- Rising_sun_lemma label "Rising sun lemma".
- Rising_sun_lemma sameAs Lemme_du_soleil_levant.
- Rising_sun_lemma sameAs m.047p9hp.
- Rising_sun_lemma sameAs Q1965964.
- Rising_sun_lemma sameAs Q1965964.
- Rising_sun_lemma sameAs Rising_sun_lemma.
- Rising_sun_lemma wasDerivedFrom Rising_sun_lemma?oldid=601452005.
- Rising_sun_lemma depiction Rising_sun_lemma.svg.
- Rising_sun_lemma isPrimaryTopicOf Rising_sun_lemma.
