diff --git a/tracial_property_gamma_v2.txt b/tracial_property_gamma_v2.txt
index 2d22aff..866352a 100644
--- a/tracial_property_gamma_v2.txt
+++ b/tracial_property_gamma_v2.txt
@@ -2625,7 +2625,7 @@ polar-decomposition argument) gives
       <= |t|^3 / (6 N^{3/2}) tau(|d|^3)
       <= 3^{3/4} |t|^3 / (6 N^{3/2})                             (taylor)
 
-The last inequality is H\"older's inequality for the probability measure
+The last inequality is Holder's inequality for the probability measure
 associated with d at tau, together with tau(|d|^3) <= tau(d^4)^{3/4}
 and (row-moments).  Inserting the two conditional moment bounds from
 (row-moments) into (taylor), for every 1 <= j <= N:
@@ -2738,7 +2738,7 @@ quantiles q_1, ..., q_{m-1} whose union U satisfies gamma(U) < theta.
 Interpolate linearly across U to get continuous f_1, ..., f_m: R -> [0, 1]
 with
 
-    sum_i f_i = 1,  f_i = 1_{I_i} on R \\ U.
+    sum_i f_i = 1,  f_i = 1_{I_i} on R minus U.
 
 Near q_i, only f_i and f_{i+1} vary: one descends from 1 to 0, the
 other its complement.  Two scalar estimates:
@@ -3727,7 +3727,7 @@ k(n) >= k give
 Taking lim_omega and letting k(n) -> omega inf:
 
     ||[f, x_k]||_{2, Lambda} = 0,
-    tau(f x_k) = c tau(x_k),\qquad tau(f - f^2) = 0.
+    tau(f x_k) = c tau(x_k);   tau(f - f^2) = 0.
 
 The projection-defect identity implies ||f - f^2||_{2, Lambda} = 0
 because (f - f^2)^2 <= f - f^2 for a positive contraction, so f^2 = f