Planck's law derivation

The derivation of Planck's law in my textbook begins with the assumption that the energy of an oscillator with frequency ##\nu## is quantised in units of ##h\nu##. It follows that the average energy of such an oscillator (in equilibrium with a reservoir at temperature ##T##) will be
[tex]<E>=\frac{h\nu}{e^{h\nu/kT}-1}.[/tex]

Then, the textbook asserts that the average energy of a mode of electromagnetic radiation with frequency ##\nu## will be the same, and I don't see why this should be true.