diff --git a/pointwise_multiple_ergodic_mixing_v2.txt b/pointwise_multiple_ergodic_mixing_v2.txt
index 058be02..a8ba4b8 100644
--- a/pointwise_multiple_ergodic_mixing_v2.txt
+++ b/pointwise_multiple_ergodic_mixing_v2.txt
@@ -290,7 +290,7 @@ converges almost everywhere as kto∞.
 Moreover, for each cin[1,2] and ε>0 there exists a standard
 averaging profile phi with
 [
- norm{phi-c^{-1}mathbf 1_bf1_{(0,c]}}_{L^1(R)}<ε.
+ norm{phi-c^{-1}1_bf1_{(0,c]}}_{L^1(R)}<ε.
 ]
 
 
@@ -334,7 +334,7 @@ For phi a profile, we have
 [
  V_k^phi(y)=sum_{linZ}2^{-k}phi(l/2^k)F_l.
 ]
-For h_c=c^{-1}mathbf 1_bf1_{(0,c]} set
+For h_c=c^{-1}1_bf1_{(0,c]} set
 [
  W_k(y)=sum_{linZ}2^{-k}h_c(l/2^k)F_l.
 ]
@@ -349,7 +349,7 @@ y.  Now pick a sequence of profiles phi^{(m)} with
 norm{h_c-phi^{(m)}}_1to0.  On a common conull set (intersection
 of the conull sets supplied by Proposition~prop:input-smooth at each
 m) all V_k^{phi^{(m)}}(y) converge.  For mto∞ the above
-display and the triangle inequality show that W_k(y) is Cauchy.  Since
+display and the triangle ineuality show that W_k(y) is Cauchy.  Since
 W_k and the ordinary average differ by O(2^{-k}), the ordinary averages
 along N_k=floor( c2^k) form a Cauchy sequence for mu-almost
 every y.  This holds for every c in a countable dense subset of
@@ -462,7 +462,7 @@ B-measurable and bounded by one; hence
  limsup_{Nto∞}|frac1Nsum_{l=1}^Nip{v_l}{v_{l+h}}|lenorm{E[F_{s,h}mid B]}_1.
 ]
 For d=1 this bound holds directly; for d>1 it is the induction output.
-The Hilbert-space van der Corput inequality bounds the size of the limit in
+The Hilbert-space van der Corput ineuality bounds the size of the limit in
 L^2 by a constant times
 [
  frac1H+frac1Hsum_{h=1}^Hnorm{E[F_{s,h}mid B]}_1.
@@ -1063,11 +1063,11 @@ integral in a pair inner product is small by INPUT A whenever the times in
 the two copies of (eq:channel-times) are sufficiently separated.  The
 times within each copy separate once l,l' exceed a fixed threshold.
 Failure of separation between copies requires one of finitely many
-inequalities
+ineualities
 [
  |e_gamma i l-e_gamma i'l'+a'|le R.
 ]
-For fixed l, each inequality permits only a bounded number of integers
+For fixed l, each ineuality permits only a bounded number of integers
 l', because e_gamma,i'>0; and symmetrically.  Their union gives a
 bounded-degree graph.  Coordinate integrals for other output indices are
 bounded by 1.  The separation threshold and L_0 may depend on eta;