  We report elastic neutron diffraction and muon spin relaxation (muSR)
measurements of the quasi one-dimensional antiferromagnets Sr2CuO3 and Ca2CuO3,
which have extraordinarily reduced TN/J ratios. We observe almost
resolution-limited antiferromagnetic Bragg reflections in Sr2CuO3 and obtain a
reduced ordered moment size of ~0.06 \muB. We find that the ratio of ordered
moment size \mu(Ca2CuO3)/\mu(Sr2CuO3)=1.5(1) roughly scales with their Neel
temperatures, which suggests that the ordered moment size of quasi
one-dimensional antiferromagnets decreases continuously in the limit of
vanishing inter-chain interactions.
