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Jan
27
accepted Is the given function injective?
Jan
27
comment Is the given function injective?
that sounds good. thx.
Jan
26
comment Is the given function injective?
I didnt understand well. For example, If $k=2$ and $a$ and $c$ are some values such that $(3)$ holds, then this $(a,a,c,c)$ will results in some $(x,y)$ for which $x=y$. But if we choose another $a$ and $c$ such that $(3)$ holds then, this time we will get another $(x,y)$ such that $x=y$. Although both will give $x=y$ this value will be different in two difference cases. Am I missing something? What are the concere $(a_1,b_1,c_1,d_1)$ and $(a_2,b_2,c_2,d_2)$ such that for both cases I get $(x_1,y_1)$ s.t. $x_1=y_1$?
Jan
25
revised Is the given function injective?
added 19 characters in body
Jan
24
revised Is the given function injective?
edited tags
Jan
24
revised Is the given function injective?
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Jan
24
comment How to encode a list of integers, how to find an arithmetical formula for a sequence?
If I were you I would use some polynomial regression. It would fit with round operation. How many terms you will have I cannot say. One needs to check
Jan
24
asked Is the given function injective?
Jan
20
revised Law of total probability explanation about sample space
added 1 character in body
Jan
19
answered Law of total probability explanation about sample space
Jan
19
answered Origin of the notation for statistical divergence
Jan
10
revised Solve for Maximum Likelihood Estimate
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Jan
4
revised Probability of a continuous random variable
added 2 characters in body; edited title
Dec
20
accepted on existence of supremum/infimum
Dec
20
comment on existence of supremum/infimum
thank you very much for the clarifications. This is exactly how I was thinking;)
Dec
20
comment on existence of supremum/infimum
one last thing. If I know that $T\in[0,1]$ for every $g$ and $T$ is a convex functional of $g$ as in the question. Would this be of any help?
Dec
20
comment on existence of supremum/infimum
okay I think I should have added the functional $T$ while I was writing the question. Sorry for that.
Dec
20
comment on existence of supremum/infimum
$X$ is not compact. what I can do is to increase the radius of the closed ball. Then it will include many other density functions. Will this help me to achive the supremum of $T$, where $T$ is a convex functional of $g$? if not what can I do? in real numbers I extend the domain(exampe 2 in the question) and I am done.
Dec
20
comment on existence of supremum/infimum
i do not ask the supremum of a set. I ask the supremum of a functional defined over this set. Analogy is the function given which was defined over real numbers. Now instead of real numbers as the domain, we have the set of density functions. Let $T$ a convex functional of $g$.
Dec
20
comment on existence of supremum/infimum
I dont get what you mean. If the space of functions are given by $X$ as in the question and if we are interested in the existence of a density function $g^*$ (f is known and given) on $X$ such that the supremum of $T$ is achieved for this $g^*$. Will I be able to guarantee the existence of such $g^*$ all the time (for any $\delta$ or even $T$). I think it is not possible. Then where should I look for such a $g^*$. I understood that supremum is more related to the completeness than it is related to the compactness. But how does it help me here?