I'd like to show that
A convex function defined on open interval is continuous.
I get the result, f is Lipschitz function on any closed subinterval.
But, I am stucked here.
How can i get the result?
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Does this answer your question? : https://math.stackexchange.com/questions/941029/is-every-convex-function-on-an-open-interval-continuous – Kavi Rama Murthy Jun 04 '20 at 09:39
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I have converted "the" into "a" ("the" would mean there is a unique convex function) – Jean Marie Jun 04 '20 at 09:39
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@Kavi Rama Murthy Yes, but i stuck there.. – Crawl Jun 04 '20 at 09:42
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Cold you tell us where exactly you have problem? – Kavi Rama Murthy Jun 04 '20 at 09:45
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I want to know the logic, if f is lipschitz on any closed subinterval, then f is continuous on open interval. – Crawl Jun 04 '20 at 09:58