Three classical functional equations. Cauchy's additive equation f(x + y) = f(x) + f(y), solved by any linear f(x) = c x under any one of: continuity at a single point, Lebesgue measurability, boundedness on a positive-measure set,…
Three classical functional equations. Cauchy's additive equation f(x + y) = f(x) + f(y), solved by any linear f(x) = c x under any one of: continuity at a single point, Lebesgue measurability, boundedness on a positive-measure set,…