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

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

limx1f(x1,x2,...,xn)=const.,a.e.inRn-1.

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

limx1f(x1,x2,...,xn)=const.,p.p.dansRn-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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {24},
     number = {3},
     year = {1974},
     pages = {159-164},
     doi = {10.5802/aif.523},
     zbl = {0292.26013},
     mrnumber = {52 \#11574},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1974__24_3_159_0}
}
Fefferman, Charles. Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$. Annales de l'Institut Fourier, Volume 24 (1974) no. 3, pp. 159-164. doi : 10.5802/aif.523. http://www.numdam.org/item/AIF_1974__24_3_159_0/

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