The electrical conductivity of a thin gas discharge gap (d = 60 mu m) filled with atmospheric air at 60 Torr pressure and room temperature was investigated. Current-voltage characteristics of the device when both the electrodes are metals and when one of the electrodes is a high resistivity GaAs semiconductor were measured. It is shown that in the device with the semiconductor electrode, the current is registered before the breakdown of gas. The value of pre-breakdown current depends on experimental conditions: it increases drastically if gas is subjected to breakdown before the measurements. Thus, the device has a memory effect. The value of memory effect depends on the value of the ionization current and does not depend on the polarity of the applied voltage. The effect is absent in a device with two metallic electrodes, and the effect disappears after the pumping of the gas down to 0.1 Torr. The obtained results can be explained on the basis of diffusion-drift type equilibrium of charges taking into account the charging of the semiconductor near the surface. The latter is the guarantee of the stability of residual pre-breakdown current in the gas.