A THEOREM OF LOHWATER AND PIRANIAN

作者：Danielyan Arthur A^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(9): 3919-3920.

DOI：10.1090/proc/13083

• Bounded analytic function
• Fatou's theorem
• radial limit
• F-sigma set

By a well-known theorem of Lohwater and Piranian, for any set E on vertical bar z vertical bar = 1 of type Fs and of measure zero there exists a bounded analytic function in vertical bar z vertical bar < 1 which fails to have radial limits exactly at the points of E. We show that this theorem is an immediate corollary of Fatou's interpolation theorem of 1906.

• 出版日期2016-9