I came to the following question, but don't have quite a good idea to approach.

Can a set $A\subset \mathbb{R}^n , n\ge 2$ with nonzero measure be in a general linear position?

I believe that, since this is quite a simple question, this would already have an answer, but I could not find it.

I came to the following question, but I don't have quite a good idea how to approach.

Can a set $A\subset \mathbb{R}^n , n\ge 2$ with nonzero measure be in a general linear position?

I believe that, since this is quite a simple question, this would already have an answer, but I could not find it.