We present a sketch of the Fourier theory on the in.nite symmetric group S _∞. As a dual space to S _∞, we suggest the space (groupoid) of Young bitableaux B. The Fourier transform of a function on the infinite symmetric group is a martingale with respect to the so-called full Plancherel measure on the groupoid of bitableaux. The Plancherel formula determines an isometry of the space l ²(S _∞, m) of square summable functions on the infinite symmetric group with the counting measure and the space L²(B,μ ̃) of square integrable functions on the groupoid of bitableaux with the full Plancherel measure.