However, it is not clear to me that the same is true for quasi-concave functions f... That is, is f|->int_(x in x)f(x)d mu quasi-concave on X is f is quasi-concave?

tramolatzqvg

tramolatzqvg

Answered question

2022-11-02

However, it is not clear to me that the same is true for quasi-concave functions f...
f x X f ( x ) d μ
quasi-concave on X is f is quasi-concave?

Answer & Explanation

Zackary Hatfield

Zackary Hatfield

Beginner2022-11-03Added 14 answers

This is not true. Take f ( x ) = | x | . This is quasi-convex. Set X = { 1 , 2 } with counting measure. Then
x R 2 f ( x 1 ) + f ( x 2 )
is not quasiconvex: The points ( 1 , 0 ), ( 0 , 1 ) are mapped to 1, their midpoint to 2 . Hence the sub-level set to level 1 is not convex.

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