We study the electronic structure of HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} (Hg1223; T_{c}=134 K) using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). Resonant valence band PES across the O K edge and Cu L edge identifies correlation satellites originating in O 2p and Cu 3d two-hole final states, respectively. Analyses using the experimental O 2p and Cu 3d partial density of states show quantitatively different on-site Coulomb energy for the Cu site (U_{dd}=6.5±0.5 eV) and O site (U_{pp}=1.0±0.5 eV). Cu_{2}O_{7}-cluster calculations with nonlocal screening explain the Cu 2p core level PES and Cu L-edge XAS spectra, confirm the U_{dd} and U_{pp} values, and provide evidence for the Zhang-Rice singlet state in Hg1223. In contrast to other hole-doped cuprates and 3d-transition metal oxides, the present results indicate weakly correlated oxygen holes in Hg1223.
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