On some problems concerning Borel structures in function spaces

It is an open problem if any separable compact space K whose function space C(K) with the cylindrical sigma-algebra is a standard measurable space, embeds in the space of the first Baire class functions on the Cantor set, with the pointwise topology. We prove that this is true for separable linearly ordered compacta. Other problems discussed in this note concern the Borel structures in C(K) generated by the norm, weak or pointwise topology in C(K). We give an example of a compact space K such that the weak and the pointwise topology generate different Borel structures in C(K).