On finite-dimension Chebyshev subspaces of spaces with an integral metric

This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces $\varphi(L)$ and $L^{p(t)}$ on the interval $I=[-1,1]$, where $\varphi(t)$ is an even nonnegative continuous nondecreasing function on the half-line $[0,+\infty)$, and the function $p(t)$ is measurable, finite, and positive almost everywhere on $I$. If $\varphi$ is an $N$-function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.