Abstract
We present a measurement of $\sigma \cdot B(W \to e \nu)$ and $\sigma \cdot B(Z^0 \to e^+e^-)$ in proton - antiproton collisions at $\sqrt{s} =1.8$ TeV using a significantly improved understanding of the integrated luminosity. The data represent an integrated luminosity of 19.7 pb$^{-1}$ from the 1992-1993 run with the Collider Detector at Fermilab (CDF). We find $\sigma \cdot B(W \to e \nu) = 2.49 \pm 0.12$~nb and $\sigma \cdot B(Z^0 \to e^+e^-) = 0.231 \pm 0.012$~nb.

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