English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Left and right-continuous functions play an important role in Real analysis,especially in Measure Theory and Integration on the real line and in Stochasticprocesses indexed by a continuous real time. Semi-continuous functions are alsoof major interest in the same way. This paper aims at presenting a usefulhandling of semi-continuous function in parallel with the way left or rightcontinuous functions are treated. For example, a lower or upper continuousfunction shares the property that it is measurable if it fails to be upper orlower continuous at most at a number of countable points with a left orright-continuous when it fails to be left or right-continuous at most at anumber of countable points. As a final result, the comparison between theRiemann and the Lebesgue integrals on compact sets is done in a verycomfortable and comprehensive way. The frame used here is open to more furthersophistication

A parallel treatment of semi-continuous functions with left and right-functions continuous and some application in pedagogy