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The dataset reaches a point-source depth of <jats:italic>I<\/jats:italic><jats:sub>E<\/jats:sub> = 28.0 (<jats:italic>Y<\/jats:italic><jats:sub>E<\/jats:sub>, <jats:italic>J<\/jats:italic><jats:sub>E<\/jats:sub>, <jats:italic>H<\/jats:italic><jats:sub>E<\/jats:sub> = 25.3), AB magnitudes at 5 <jats:italic>\u03c3<\/jats:italic> with a 0\u2032\u2032.16 (0\u2032\u2032.48) full width at half maximum (FWHM), and a surface brightness limit of 30.1 (29.2) mag arcsec<jats:sup>\u22122<\/jats:sup> for radially integrated galaxy profiles. The exceptional depth and spatial resolution of this wide-field multi-band data enable simultaneous detection and characterisation of both bright galaxies and low surface brightness ones, along with their globular cluster systems, from the optical to the near-infrared (NIR). Cluster membership was determined using several methods in order to maximise the completeness and minimise the contamination of foreground and background sources. We adopted a catalogue of 1100 dwarf galaxies, detailed in the corresponding ERO paper, that includes their photometric and structural properties. We identified all other sources in the <jats:italic>Euclid<\/jats:italic> images and obtained accurate photometric measurements using <jats:monospace>AutoProf<\/jats:monospace> or <jats:monospace>AstroPhot<\/jats:monospace> for 137 bright cluster galaxies and <jats:monospace>SourceExtractor<\/jats:monospace> for half a million compact sources. This study advances beyond previous analyses of the cluster and enables a range of scientific investigations, which are summarised here. We derived the luminosity and stellar mass functions (LF and SMF) of the Perseus cluster in the <jats:italic>Euclid<\/jats:italic> <jats:italic>I<\/jats:italic><jats:sub>E<\/jats:sub> band thanks to supplementary <jats:italic>u, g, r, i, z<\/jats:italic>, and H<jats:italic>\u03b1<\/jats:italic> data from the Canada-France-Hawai\u2019i Telescope (CFHT). Our LF and SMF are the deepest recorded for the Perseus cluster, highlighting the groundbreaking capabilities of the <jats:italic>Euclid<\/jats:italic> telescope. We fit the LF and SMF with a Schechter plus Gaussian model. The LF features a dip at <jats:italic>M<\/jats:italic>(<jats:italic>I<\/jats:italic><jats:sub>E<\/jats:sub>) \u2243 \u221219 and a faint-end slope of <jats:italic>\u03b1<\/jats:italic><jats:sub>S<\/jats:sub> \u2243 \u22121.2 to \u22121.3. The SMF displays a low-mass-end slope of <jats:italic>\u03b1<\/jats:italic><jats:sub>S<\/jats:sub> \u2243 \u22121.2 to \u22121.35. These observed slopes are flatter than those predicted for dark matter halos in cosmological simulations, offering significant insights for models of galaxy formation and evolution.<\/jats:p>","DOI":"10.1051\/0004-6361\/202450808","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T20:52:34Z","timestamp":1742503954000},"page":"A11","source":"Crossref","is-referenced-by-count":19,"title":["<i>Euclid<\/i>: Early Release Observations \u2013 Overview of the Perseus cluster and analysis of its luminosity and stellar mass functions\u2605"],"prefix":"10.1051","volume":"697","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3263-8645","authenticated-orcid":false,"given":"J.-C.","family":"Cuillandre","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3278-4607","authenticated-orcid":false,"given":"M.","family":"Bolzonella","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9795-6433","authenticated-orcid":false,"given":"A.","family":"Boselli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1442-2947","authenticated-orcid":false,"given":"F. 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