Simultaneous EUV and X-ray variability of NGC 4051

We present a flux variability study of simultaneous RXTE and EUVE observations of the highly variable Seyfert galaxy NGC 4051. We find a strong correlation between variability in the EUV and medium-energy X-ray bands, indicating that both are sampling the same power-law continuum. The lag between the two bands is less than 20 ks and, depending on model assumptions, may be < 1 ks. We examine the consequences of such a small lag in the context of simple Comptonization models for the production of the power-law continuum. A lag of < 1 ks implies that the size of the Comptonizing region is less than 20 Schwarzschild radii for a black hole of mass > 10(6) M..