2025/10/31 by Arroyo-Rabasa, Adolfo, Conti, Sergio
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.27360
We prove that a locally integrable function f:(a,b) → \mathbb R must be affine if its mean oscillation, considered as a function of intervals, can be extended to a locally finite Borel measure. In particular, we show that any function f satisfying the integro-differential identity |Df|(I)=4osc(f,I) for all intervals I ⊂ (a,b) must be affine.