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On the average of continuous functions $f:\mathbb{R}^2\rightarrow\mathbb{R}$^2\rightarrow[0,1]$
Is it true that if the average of a continuous function $f:\mathbb{R}^2\rightarrow\mathbb{R}$$f:\mathbb{R}^2\rightarrow[0,1]$ over a unit circle centered around $(x,y)$ is $f(x,y)$ for all $(x,y)\in\mathbb{R}^2$, then $f$ is necessarily constant?
On the average of continuous functions $f:\mathbb{R}^2\rightarrow\mathbb{R}$
Is it true that if the average of a continuous function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ over a unit circle centered around $(x,y)$ is $f(x,y)$ for all $(x,y)\in\mathbb{R}^2$, then $f$ is necessarily constant?
On the average of continuous functions $f:\mathbb{R}^2\rightarrow[0,1]$
Is it true that if the average of a continuous function $f:\mathbb{R}^2\rightarrow[0,1]$ over a unit circle centered around $(x,y)$ is $f(x,y)$ for all $(x,y)\in\mathbb{R}^2$, then $f$ is necessarily constant?
On the average of continuous functions $f:\mathbb{R}^2\rightarrow\mathbb{R}$
Is it true that if the average of a continuous function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ over a unit circle centered around $(x,y)$ is $f(x,y)$ for all $(x,y)\in\mathbb{R}^2$, then $f$ is necessarily constant?
