  We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the
idea of distribution of a positive selfadjoint operator. Classical results on
R\'enyi and Kullback-Leibler divergences are applied to obtain new results and
new proofs for some known results about Petz-R\'enyi and Umegaki relative
entropy. Most important among these, is a necessary and sufficient condition
for the finiteness of the Petz-R\'enyi $\alpha$-relative entropy. All of the
results presented here are valid in both finite and infinite dimensions. In
particular, these results are valid for states in Fock spaces and thus are
applicable to continuous variable quantum information theory.
