This letter presents the analyses of a single-user beamspace multiple-input-multiple-output (MIMO) on measured indoor and outdoor channels at 142 GHz. The rank is evaluated under different antenna sizes, number of beams, and thresholds. We assume a total power constraint at the transmitter that results in a decrease in a signal-to-noise ratio as the link distance increases. When using spatial multiplexing, the indoor and outdoor sites demonstrate an average capacity gain of 2× and 1.5× at link distances below 60 m. Also, the rank for our measured 142 GHz channels is comparable to that at 60 GHz channels but significantly lower than the rank at 5 GHz channels reported in the literature. We also found that at 142 GHz, the indoor and outdoor sites have median ranks of 3.0 and 1.7 for the small-antenna case, and 4.9 and 2.4 for the large-antenna case assuming a rank threshold of 20 dB. The indoor site has a rank higher by 1.8 than the outdoor site, regardless of the antenna size. The rank decreases by only 20% and 15% for indoor and outdoor scenarios when the beam density is halved, allowing a significant reduction in implementation complexity of the beamspace MIMO without remarkably reducing the rank.