A conventional thin membrane of aerogel, although achieving a low refractive index, retains some difficulty when it is to be applied to display apparatuses or the like, because of its low strength. Membranes produced by other methods are difficult to simultaneously achieve low refractive index and sufficient strength. The present invention provides an anti-reflecting membrane which is formed at least on one side of a plate transmitting visible light, is composed of fine inorganic oxide particles and a binder, contains a number of pores inside, and has an arithmetic average surface roughness (Ra) below 6 nm. The present invention also provides preferred embodiments of the display apparatuses provided with the membrane.