Is there any definition for locally measurable functions similar to locally continuity ?

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- January 14th 2008, 11:38 PMmazaherilocally measurable functions
Is there any definition for locally measurable functions similar to locally continuity ?

- January 18th 2008, 04:43 AMRebesques
...What is local continuity? (Tmi)

- January 19th 2008, 06:45 AMmazaherilocally measurable functions
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 .