This theorem of real analysis describes the discontinuities of a monotone real-valued function of a real variable: every such discontinuity is necessarily a jump discontinuity, and there are at most countably many of them. The result usually appears in the literature with no attached name, though some recent works call it Froda's theorem after Alexandru Froda, who stated in his 1929 dissertation that the result was already well known and offered his own elementary proof for convenience; earlier work on the discontinuities of such functions had already appeared in an 1875 memoir by the French mathematician Jean Gaston Darboux. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Statement FormCharacterization Theorem 1 Connections
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In Branch
Source Discontinuities of Monotone Functions (Wikipedia)
Proved By
Source Discontinuities of Monotone Functions (Wikipedia)
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1. Discontinuities of Monotone Functions (Wikipedia)
Lead section
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.
Proved By: Alexandru Froda, Lead
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.
In Branch: Analysis, Lead paragraph
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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