[en] The need for a muon number conservation law separate from lepton number conservation is mandated by the absence of neutrinoless muon-electron transitions. The form of the muon number conservation law, however, is not determined by these considerations. A search was made for electron antineutrinos coming from positive muon decays, which would be allowed by a multiplicative formulation of muon number conservation, but not by an additive formulation. The LAMPF beam dump was used as a source of positive muons decaying at rest; electron antineutrinos were detected via inverse beta decay in a six-ton water Cerenkov counter. No excess of events above known backgrounds was seen; a limit was placed on the branching ratio for positive muon decay to electron antineutrinos of R < 6.5%. Electron neutrinos from normal muon decay were detected during a fill of the counter with heavy water, via the inverse beta decay on the deuteron. The cross section for this reaction was measured, averaged over the neutrino energy spectrum; the measured value of (0.52 +- 0.18) x 10^-40 cm² is in good agreement with the calculated value of 0.48 x 10^-40 cm²