Dimension of gradient measures
classification
🧮 math.CA
keywords
coordinatesderivativesdifferentdimensionmeasuresrespectfunctiongradient
read the original abstract
We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of different order.
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