  Measuring the diffuse Galactic gamma-ray flux in the TeV range is difficult
for ground-based gamma-ray telescopes because of the residual cosmic-ray
background, which is higher than the gamma-ray flux by several orders of
magnitude. Its detection is also challenging for space-based telescopes because
of low signal statistics. We characterize the diffuse TeV flux from the Galaxy
using decade-long exposures of the Fermi Large Area Telescope. Considering that
the level of diffuse Galactic emission in the TeV band approaches the level of
residual cosmic-ray background, we estimated the level of residual cosmic-ray
background in the SOURCEVETO event selection and verified that the TeV diffuse
Galactic emission flux is well above the residual cosmic-ray background up to
high Galactic latitude regions. We study spectral and imaging properties of the
diffuse TeV signal from the Galactic plane. We find much stronger emission from
the inner Galactic plane than in previous HESS telescope estimates (lower
bound). We also find a significant difference in the measurement of the
Galactic longitude and latitude profiles of the signal measured by Fermi and
HESS. These discrepancies are presumably explained by the fact that regions of
background estimate in HESS have non-negligible gamma-ray flux. Comparing Fermi
measurements with those of ARGO-YBJ, we find better agreement, with the notable
exception of the Cygnus region, where we find much higher flux (by a factor
1.5). We also measure the TeV diffuse emission spectrum up to high Galactic
latitude and show that the spectra of different regions of the sky have
spectral slopes consistent with Gamma=2.34+/- 0.04. We discuss the possible
origin of the hard slope of the TeV diffuse emission. Fermi/LAT provides
reliable measurements of the diffuse Galactic emission spectrum in the TeV
range.
