Subsets of full measure in a generic submanifold in are non-plurithin

In this paper we prove that if is a subset of measure in a -smooth generic submanifold , then is non-plurithin at each point of in . This result improves a previous result of A. Edigarian and J. Wiegerinck who considered the case where is pluripolar set contained in a -smooth generic submanifold (Edigarian and Wiegernick in Math. Z. 266(2):393–398, 2010 ). The proof of our result is essentially different.