Continuous pseudocharacters on connected locally compact groups are characters (Q1337923)

The author proves that any continuous pseudocharacter on a connected locally compact group \(G\) (that is a real function \(f\) with \(f(x^n) = nf(x)\) and the set \(\{f(xy) - f(x) - f(y) : x,y \in G\}\) is bounded) is a continuous homomorphism of \(G\) into \(\mathbb{R}\).