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Determining the average fraction of Lyman continuum (LyC) photons escapinghigh redshift galaxies is essential for understanding how reionizationproceeded in the z>6 Universe. We want to measure the LyC signal from a sampleof sources in the Chandra Deep Field South (CDFS) and COSMOS fields for whichultra-deep VIMOS spectroscopy as well as multi-wavelength Hubble SpaceTelescope (HST) imaging are available.  We select a sample of 46 galaxies at $z\sim 4$ from the VIMOS Ultra DeepSurvey (VUDS) database, such that the VUDS spectra contain the LyC part of thespectra, that is, the rest-frame range $880-910\AA$. Taking advantage of theHST imaging, we apply a careful cleaning procedure and reject all the sourcesshowing nearby clumps with different colours, that could potentially belower-redshift interlopers. After this procedure, the sample is reduced to 33galaxies. We measure the ratio between ionizing flux (LyC at $895\AA$) andnon-ionizing emission (at $\sim 1500 \AA$) for all individual sources. We alsoproduce a normalized stacked spectrum of all sources. Assuming an intrinsicaverage $L_{\nu}(1470)/L_{\nu}(895)$ of 3, we estimate the individual andaverage relative escape fraction. We do not detect ionizing radiation from anyindividual source, although we identify a possible LyC emitter with very highLy$\alpha$ equivalent width (EW). From the stacked spectrum and assuming a meantransmissivity for the sample, we measure a relative escape fraction$f_{esc}^{rel}=0.09\pm0.04$. We also look for correlations between the limitsin the LyC flux and source properties and find a tentative correlation betweenLyC flux and the EW of the Ly$\alpha$ emission line.  Our results imply that the LyC flux emitted by $V=25-26$ star-forminggalaxies at z$\sim$4 is at most very modest, in agreement with previous upperlimits from studies based on broad and narrow band imaging.

New constraints on the average escape fraction of Lyman continuum radiation in z~4 galaxies from the VIMOS Ultra Deep Survey (VUDS)