Vela X is a region of extended radio emission in the western part of the Vela constellation: one of the nearest pulsar wind nebulae (PWNe), and associated with the energetic Vela pulsar (PSR B0833-45). Extended very-high-energy (VHE) $gamma$-ray emission (HESS $mathrm{J0835mhyphen 455}$) was discovered using the H.E.S.S. experiment in 2004. The VHE $gamma$-ray emission was found to be coincident with a region of X-ray emission discovered with ${it ROSAT}$ above 1.5 keV (the so-called textit{Vela X cocoon}): a filamentary structure extending southwest from the pulsar to the centre of Vela X. A deeper observation of the entire Vela X nebula region, also including larger offsets from the cocoon, has been performed with H.E.S.S. This re-observation was carried out in order to probe the extent of the non-thermal emission from the Vela X region at TeV energies and to investigate its spectral properties. In order to increase the sensitivity to the faint $gamma$-ray emission from the very extended Vela X region, a multivariate analysis method combining three complementary reconstruction techniques of Cherenkov-shower images is applied for the selection of $gamma$-ray events. The analysis is performed with the On/Off background method, which estimates the background from separate observations pointing away from Vela X; towards regions free of $gamma$-ray sources but with comparable observation conditions. The $gamma$-ray surface brightness over the large Vela X region reveals that the detection of non-thermal VHE $gamma$-ray emission from the PWN HESS $mathrm{J0835mhyphen 455}$ is statistically significant over a region of radius 1.2$^{circ}$ around the position $alpha$ = 08$^{mathrm{h}}$ 35$^{mathrm{m}}$ 00$^{mathrm{s}}$, $delta$ = -45$^{circ}$ 36$^{mathrm{prime}}$ 00$^{mathrm{prime}mathrm{prime}}$ (J2000).
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