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The combination of a large field of view, high sensitivity, and wide wavelength coverage provides an order of magnitude improvement in spectroscopically confirmed redshifts in the HUDF; i.e., 1206 secure spectroscopic redshifts for <jats:italic>Hubble <\/jats:italic>Space Telescope (HST) continuum selected objects, which corresponds to 15% of the total (7904). The redshift distribution extends well beyond <jats:italic>z<\/jats:italic>&gt; 3 and to HST\/<jats:italic>F775W <\/jats:italic>magnitudes as faint as \u2248 30 mag (AB, 1<jats:italic>\u03c3<\/jats:italic>). In addition, 132 secure redshifts were obtained for sources with no HST counterparts that were discovered in the MUSE data cubes by a blind search for emission-line features. In total, we present 1338 high quality redshifts, which is a factor of eight increase compared with the previously known spectroscopic redshifts in the same field. We assessed redshifts mainly with the spectral features [O\u2009<jats:sc>ii<\/jats:sc>] at <jats:italic>z<\/jats:italic>&lt; 1.5 (473 objects) and Ly<jats:italic>\u03b1<\/jats:italic> at 2.9 &lt;<jats:italic>z<\/jats:italic>&lt; 6.7 (692 objects). With respect to <jats:italic>F775W <\/jats:italic>magnitude, a 50% completeness is reached at 26.5 mag for ultra deep and 25.5 mag for deep fields, and the completeness remains \u2273 20% up to 28\u201329 mag and \u2248 27 mag, respectively. We used the determined redshifts to test continuum color selection (dropout) diagrams of high-<jats:italic>z<\/jats:italic> galaxies. The selection condition for <jats:italic>F336W <\/jats:italic>dropouts successfully captures \u2248 80% of the targeted <jats:italic>z<\/jats:italic> ~ 2.7 galaxies. However, for higher redshift selections (<jats:italic>F435W<\/jats:italic>, <jats:italic>F606W<\/jats:italic>, and <jats:italic>F775W <\/jats:italic>dropouts), the success rates decrease to \u2248 20\u201340%. We empirically redefine the selection boundaries to make an attempt to improve them to \u2248 60%. The revised boundaries allow bluer colors that capture Ly<jats:italic>\u03b1<\/jats:italic> emitters with high Ly<jats:italic>\u03b1<\/jats:italic> equivalent widths falling in the broadbands used for the color-color selection. Along with this paper, we release the redshift and line flux catalog. <\/jats:p>","DOI":"10.1051\/0004-6361\/201731195","type":"journal-article","created":{"date-parts":[[2017,10,11]],"date-time":"2017-10-11T18:36:19Z","timestamp":1507746979000},"page":"A2","source":"Crossref","is-referenced-by-count":165,"title":["The MUSE <i>Hubble <\/i>Ultra Deep Field Survey"],"prefix":"10.1051","volume":"608","author":[{"given":"H.","family":"Inami","sequence":"first","affiliation":[]},{"given":"R.","family":"Bacon","sequence":"additional","affiliation":[]},{"given":"J.","family":"Brinchmann","sequence":"additional","affiliation":[]},{"given":"J.","family":"Richard","sequence":"additional","affiliation":[]},{"given":"T.","family":"Contini","sequence":"additional","affiliation":[]},{"given":"S.","family":"Conseil","sequence":"additional","affiliation":[]},{"given":"S.","family":"Hamer","sequence":"additional","affiliation":[]},{"given":"M.","family":"Akhlaghi","sequence":"additional","affiliation":[]},{"given":"N.","family":"Bouch\u00e9","sequence":"additional","affiliation":[]},{"given":"B.","family":"Cl\u00e9ment","sequence":"additional","affiliation":[]},{"given":"G.","family":"Desprez","sequence":"additional","affiliation":[]},{"given":"A. 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