Is there any definition for locally measurable functions similar to locally continuity ?
Let's X be a measurable set and Y be a topological space. f is a function,
f: X -----> Y. Similarly to locally continuity, f may be defined measurable in point x0 of X if for every neighborhood V of f(x0) ,there is a measurable set W containing x0 such that f(W) is subset of V .