I do have a quick question: if I have a distribution $f(x)$ over the real line where the support is the whole line, does the Shannon Entrophy uniquely characterise f ? I.e do we have $H(f) = H(f^*)$ is implies that $f = f^*$  ?(the reverse is obviously true).

If I have a distribution $f(x)$ over the real line where the support is the whole line, does the Shannon Entropy uniquely characterise $f$? I.e., do we have $H(f) = H(f^*)$ implies $f = f^*$?  (The reverse is obviously true.)

I do have a quick question: if I have a distribution $f(x)$ over the real line where the support is the whole line, does the Shannon Entrophy uniquely characterise f ? I.e do we have $H(f) = H(f^*)$ is implies that $f = f^*$ ?(the reverse is obviously true).

Thanks in advance,

I do have a quick question: if I have a distribution $f(x)$ over the real line where the support is the whole line, does the Shannon Entrophy uniquely characterise f ? I.e do we have $H(f) = H(f^*)$ is implies that $f = f^*$ ?(the reverse is obviously true).