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What's the relationship of $f$ and $h$ in $mathbbE_i left[ f(g(x,i)) right] = h(mathbbE_i left[ g(x,i) right] )$

Characters on $Cleft( mathbbR^nright)$Proving that $xmapsto sum_yin Acapleft(0,xright]rleft(yright)$ is right-continuousUpdated: Constructing a bijection between $left(-fracpi2, fracpi2right]$ and $mathbbR$Proving that the set of differentiable functions with $left|f'(t)right|leq K$ is dense in the set of Lipschitz continuous functions?$ J = displaystyleint_0^1 left(left(y'right)^2-a^2y^2right)dx $ and $ J_1= displaystyleint_0^1 left(y' + ay tan bxright)^2dx$Linear combination of the identity and function with nonnegative derivativeHow can I show that $gleft[ a,bright] rightarrow mathbbR$ is continuous?Proving $int_A f(x,y) dxdy = left(int_a^b phi(x) dxright)left(int_c^d psi(y) dyright)$Approaching a continuous function with polynomials satisfying $left|P_nleft(xright)-fleft(xright)right|<frac2n$Solve the ode $W^prime left( sright) -2iHleft( sright) Wleft( sright) -1=0$

0

$begingroup$

Let there be a function $f$ and $h$ satisfying

$mathbbE_i left[ f(g(x,i)) right] = h(mathbbE_i left[ g(x,i) right] )$

for an arbitrary 2-variable function $g : mathbbR^n times mathbbR rightarrow mathbbR$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  please clarify what $x$ and $i$ are.
  $endgroup$
  – Cettt
  Mar 22 at 13:48
  

  
  
  
  

add a comment | 

0

$begingroup$

Let there be a function $f$ and $h$ satisfying

$mathbbE_i left[ f(g(x,i)) right] = h(mathbbE_i left[ g(x,i) right] )$

for an arbitrary 2-variable function $g : mathbbR^n times mathbbR rightarrow mathbbR$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  please clarify what $x$ and $i$ are.
  $endgroup$
  – Cettt
  Mar 22 at 13:48
  

  
  
  
  

add a comment | 

$begingroup$

Let there be a function $f$ and $h$ satisfying

$mathbbE_i left[ f(g(x,i)) right] = h(mathbbE_i left[ g(x,i) right] )$

for an arbitrary 2-variable function $g : mathbbR^n times mathbbR rightarrow mathbbR$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

asked Mar 22 at 13:45

JunhoJunho

115

asked Mar 22 at 13:45

JunhoJunho

115