Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities
Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities
Using the continuum hypothesis, SierpiÅski constructed a nonmeasurable function $f$ such that $\{ h: f(x+h)\ne f(x-h)\}$ is countable for every $x.$ Clearly, such a function is symmetrically approximately continuous everywhere. Here we to show that SierpiÅskiâs example cannot be constructed in ZFC. Moreover, we show it is consistent with ZFC …