Explain in words an assumption on a function

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Consider a function $(X,epsilon)mapsto f(X,epsilon)$ where



  • $X$ is a vector $Ktimes 1$ belonging to $mathbbR^K$


  • $epsilon$ is a vector $Mtimes 1$ belonging to $mathbbR^M$


  • $f(X,epsilon)in mathbbR$


I would like your help to explain in words the following assumption:



$$
(star) hspace1cm f(X,epsilon)equiv g(X)+v(epsilon)
$$
with $g: mathbbR^Krightarrow mathbbR$ and $v: mathbbR^Mrightarrow mathbbR$.



Is it correct to say "It is assumed that $f$ is additively separable over $X$ and $epsilon$"? I am not convinced about it. Do you have better suggestions?




functions terminology




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  • 1




    I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
    – Sobi
    Aug 27 at 16:10










  • I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
    – poetasis
    Aug 27 at 16:49














up vote
1
down vote

favorite












Consider a function $(X,epsilon)mapsto f(X,epsilon)$ where



  • $X$ is a vector $Ktimes 1$ belonging to $mathbbR^K$


  • $epsilon$ is a vector $Mtimes 1$ belonging to $mathbbR^M$


  • $f(X,epsilon)in mathbbR$


I would like your help to explain in words the following assumption:



$$
(star) hspace1cm f(X,epsilon)equiv g(X)+v(epsilon)
$$
with $g: mathbbR^Krightarrow mathbbR$ and $v: mathbbR^Mrightarrow mathbbR$.



Is it correct to say "It is assumed that $f$ is additively separable over $X$ and $epsilon$"? I am not convinced about it. Do you have better suggestions?




functions terminology




share|cite|improve this question


















  • 1




    I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
    – Sobi
    Aug 27 at 16:10










  • I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
    – poetasis
    Aug 27 at 16:49












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Consider a function $(X,epsilon)mapsto f(X,epsilon)$ where



  • $X$ is a vector $Ktimes 1$ belonging to $mathbbR^K$


  • $epsilon$ is a vector $Mtimes 1$ belonging to $mathbbR^M$


  • $f(X,epsilon)in mathbbR$


I would like your help to explain in words the following assumption:



$$
(star) hspace1cm f(X,epsilon)equiv g(X)+v(epsilon)
$$
with $g: mathbbR^Krightarrow mathbbR$ and $v: mathbbR^Mrightarrow mathbbR$.



Is it correct to say "It is assumed that $f$ is additively separable over $X$ and $epsilon$"? I am not convinced about it. Do you have better suggestions?




functions terminology




share|cite|improve this question














Consider a function $(X,epsilon)mapsto f(X,epsilon)$ where



  • $X$ is a vector $Ktimes 1$ belonging to $mathbbR^K$


  • $epsilon$ is a vector $Mtimes 1$ belonging to $mathbbR^M$


  • $f(X,epsilon)in mathbbR$


I would like your help to explain in words the following assumption:



$$
(star) hspace1cm f(X,epsilon)equiv g(X)+v(epsilon)
$$
with $g: mathbbR^Krightarrow mathbbR$ and $v: mathbbR^Mrightarrow mathbbR$.



Is it correct to say "It is assumed that $f$ is additively separable over $X$ and $epsilon$"? I am not convinced about it. Do you have better suggestions?





functions terminology





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 27 at 16:42









J.-E. Pin

17.4k21753




17.4k21753










asked Aug 27 at 16:06









TEX

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8019







  • 1




    I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
    – Sobi
    Aug 27 at 16:10










  • I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
    – poetasis
    Aug 27 at 16:49












  • 1




    I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
    – Sobi
    Aug 27 at 16:10










  • I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
    – poetasis
    Aug 27 at 16:49







1




1




I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
– Sobi
Aug 27 at 16:10




I don't know if there is any standard wording for this, but I quite like your suggestion. Just make sure that you provide the reader with $(star)$ the first time that you use this wording in your work.
– Sobi
Aug 27 at 16:10












I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
– poetasis
Aug 27 at 16:49




I think assumptions are generally worded: "Let x be a something-or-other where something-else-is-true... ." Definitions are important if the terms are not obvious.
– poetasis
Aug 27 at 16:49















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