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In the first year of the TESS survey, a steady progress was made in achieving the mission\u2019s primary science goal of establishing bulk densities for 50 planets smaller than Neptune. During that year, the TESS\u2019s observations were focused on the southern ecliptic hemisphere, resulting in the discovery of three mini-Neptunes orbiting the star TOI-125, a V\u00a0=\u00a011.0 K0 dwarf. We present intensive HARPS radial velocity observations, yielding precise mass measurements for TOI-125b, TOI-125c, and TOI-125d. TOI-125b has an orbital period of 4.65\u00a0d, a radius of 2.726\u00a0\u00b1\u00a00.075 RE, a mass of 9.50\u00a0\u00b1\u00a00.88\u00a0ME, and is near the 2:1 mean motion resonance with TOI-125c at 9.15\u00a0d. TOI-125c has a similar radius of 2.759\u00a0\u00b1\u00a00.10\u00a0RE and a mass of 6.63\u00a0\u00b1\u00a00.99\u00a0ME, being the puffiest of the three planets. TOI-125d has an orbital period of 19.98\u00a0d and a radius of 2.93\u00a0\u00b1\u00a00.17\u00a0RE and mass 13.6\u00a0\u00b1\u00a01.2\u00a0ME. For TOI-125b and d, we find unusual high eccentricities of 0.19\u00a0\u00b1\u00a00.04 and $0.17^{+0.08}_{-0.06}$, respectively. Our analysis also provides upper mass limits for the two low-SNR planet candidates in the system; for TOI-125.04 (RP\u00a0= 1.36\u00a0RE, P\u00a0=\u00a00.53\u00a0d), we find a 2\u03c3 upper mass limit of 1.6\u00a0ME, whereas TOI-125.05 ($R_P=4.2^{+2.4}_{-1.4}$\u00a0RE, P\u00a0= 13.28\u00a0d) is unlikely a viable planet candidate with an upper mass limit of 2.7\u00a0ME. We discuss the internal structure of the three confirmed planets, as well as dynamical stability and system architecture for this intriguing exoplanet system.<\/jats:p>","DOI":"10.1093\/mnras\/staa197","type":"journal-article","created":{"date-parts":[[2020,1,22]],"date-time":"2020-01-22T20:10:08Z","timestamp":1579723808000},"page":"5399-5412","source":"Crossref","is-referenced-by-count":36,"title":["Mass determinations of the three mini-Neptunes transiting TOI-125"],"prefix":"10.1093","volume":"492","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5254-2499","authenticated-orcid":false,"given":"L D","family":"Nielsen","sequence":"first","affiliation":[{"name":"Geneva Observatory, University of Geneva, Chemin des Mailettes 51, CH-1290 Versoix, Switzerland"}]},{"given":"D","family":"Gandolfi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universita degli Studi di Torino, via Pietro Giuria 1, I-10125 Torino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5080-4117","authenticated-orcid":false,"given":"D J","family":"Armstrong","sequence":"additional","affiliation":[{"name":"Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK"},{"name":"Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2733-8725","authenticated-orcid":false,"given":"J S","family":"Jenkins","sequence":"additional","affiliation":[{"name":"Departamento de Astronom\u00eda, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile"}]},{"given":"M","family":"Fridlund","sequence":"additional","affiliation":[{"name":"Leiden Observatory, PO Box 9513, NL-2300 RA Leiden, the Netherlands"},{"name":"Department of Space, Earth and Environment, Chalmers University of Technology Onsala Space Observatory, Onsala, SE-439 92, Sweden"}]},{"given":"N C","family":"Santos","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP, Rua das Estrelas, P-4150-762 Porto, Portugal"},{"name":"Departamento de F\u00edsica e Astronomia, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre, P-4169-007 Porto, Portugal"}]},{"given":"F","family":"Dai","sequence":"additional","affiliation":[{"name":"Division of Geological and Planetary Sciences, California Institute of Technology, 1200 East California Blvd, Pasadena, CA 91125, USA"}]},{"given":"V","family":"Adibekyan","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Universidade do Porto, CAUP, Rua das Estrelas, P-4150-762 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4671-2957","authenticated-orcid":false,"given":"R","family":"Luque","sequence":"additional","affiliation":[{"name":"Instituto de Astrofisica de Canarias, Calle V\u00eda L\u00e1ctea, s\/n, E-38205 San Crist\u00f3bal de La Laguna, Santa Cruz de Tenerife, Spain"},{"name":"Dpto. 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