diff --git a/planar_xy_spin_field_v2.txt b/planar_xy_spin_field_v2.txt
index 24da39f..3b0f160 100644
--- a/planar_xy_spin_field_v2.txt
+++ b/planar_xy_spin_field_v2.txt
@@ -1561,7 +1561,7 @@ continuum field and identify its moments and law.
 
 Throughout, S_n^sigma(f) = n^{-2} sum_{x in D_n^o} f(x) W_n^sigma(x),
 sigma in {-1,1}, with W_n^sigma as in Section 8; thus S_n^+ = S_n and
-S_n^-(f) = overline{S_n^+(overline f)}. The same convention is used
+S_n^-(f) = S_n^+(overline f). The same convention is used
 for continuum fields: the minus sign conjugates the field, and
 conjugating an evaluation conjugates its test function.
 
@@ -1894,7 +1894,7 @@ moment bounds as Z, hence is exponentially integrable and has the
 same characteristic function as Z. The Cramer-Wold criterion
 identifies the vector law. Every convergent subsequence has this law,
 proving full-sequence convergence. For the stated mixed moments use
-overline{S_n(f)} = S_n^-(overline f) in Proposition 10.4. []
+S_n(f) = S_n^-(overline f) in Proposition 10.4. []
 
 PROPOSITION 10.6 (tightness in the local Sobolev topology). The laws
 of S_n are tight in H^{-3}_loc(D) and converge there along the full