The statement to prove is:

$E_{L_{2}f}(x) = E_{L f}(x)$

It looks like the expression involves the expected value (denoted by $E$) of some function, and there is a composition of two functions, $L_2f$ and $Lf$. Without more context or definitions of $L$, $L_2$, and $f$, it is difficult to proceed with a formal proof.

Could you provide more details about the functions $L_2$, $L$, and how the expected value operator $E$ is defined here? This might involve definitions related to transformations or operators acting on functions.

Feel free to upload any additional context or clarify any specific details of the problem setup.

Here are some follow-up questions that might help clarify or extend the proof:

1. How are the operators $L$ and $L_2$ defined in this context?
2. Is the expected value operator $E$ in this problem the standard probabilistic expectation, or is it defined differently?
3. What is the domain and range of the function $f$?
4. Could this problem be related to differential operators or linear transformations?
5. Are there any known properties of the operators $L$ and $L_2$ that we can use in the proof?

Tip: When tackling proofs, especially with operators, reviewing the fundamental definitions is critical before proceeding with detailed calculations.