Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

Recently I came across the following statement:

What happens when a convex function f achieves the value −1 at some point xo? Usually, a degenerate behaviour occurs. For instance, suppose that f is defined on R, and f(0) =

− infinity. If f(1) is finite (say), then onehave f(x) = −1 for all 0 <= x < 1 and f(x) = +infinity for all x > 1.must

Apparently there is no restriction on the function characteristics, e.g. continuity, on f, why is it a "MUST"? If f is continuous (is this allowed for extended real-valued function?), it seems this is not a "MUST".

Or please kindly advise me on the definition of extended real-valued function as well as its characteristics.

Thanks very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Extended real-valued function

**Physics Forums | Science Articles, Homework Help, Discussion**