• Corpus ID: 248887838

Spatial-Temporal Differentiation Theorems

  title={Spatial-Temporal Differentiation Theorems},
  author={Idris Assani and Aidan Young},
where (Fk) ∞ k=1 is a sequence of measurable sets Fk ∈ B with positive measure μ(Fk) > 0; specifically, we consider questions of when this limit exists, and when it exists, what that limit is for f ∈ L(X, μ). Before proceeding, we pause to distinguish these problems from two other kinds of differentiation problems which we will call temporal and spatial differentiation problems. A temporal differentiation problem might look like limk→∞ 1 k ∑ k−1 i=0 ∫ Ti f dμ, and a spatial differentiation… 
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