Convergence on almost every line for functions with gradient in L p (𝐑 n )
Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 159-164.

On démontre que si grad (f)∈L p (R n ) pour certaines valeurs de p, alors

lim x 1 → ∞ f ( x 1 , x 2 , ... , x n ) = const., p.p. dans R n - 1 .

We prove that if grad (f)∈L p (R n ) for certain values of p, then

lim x 1 → ∞ f ( x 1 , x 2 , ... , x n ) = const., a.e. in R n - 1 . 

@article{AIF_1974__24_3_159_0,
     author = {Fefferman, Charles},
     title = {Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$},
     journal = {Annales de l'Institut Fourier},
     pages = {159--164},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {3},
     year = {1974},
     doi = {10.5802/aif.523},
     mrnumber = {52 #11574},
     zbl = {0292.26013},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.523/}
}
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Fefferman, Charles. Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$. Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 159-164. doi : 10.5802/aif.523. http://www.numdam.org/articles/10.5802/aif.523/

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[3] V. Portnov, Doklady AN SSSR, to appear.

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