$$X=\mathbb C^n\qquad d_p(x,y)=\left(\sum_{i-1}^n\left|x_i-y_i\right|^p\right)^{1/p}$$

$$x=(x_1,\ldots,x_n),y=(y_1,\ldots,y_n)\in\mathbb C^n$$

Is this a metric space, if $0 < p < 1$?
I know the answer is yes, if $p>1$, but in this case, I am not really sure.


Take $n=2$; then $d_p((1,0),(0,1))=(1+1)^2=4$

But: $d_p((1,0),(1,1))+d_p((1,1),(0,1))=1^2+1^2=2<4$


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