Spatial-temporal differentiation theorems
نویسندگان
چکیده
Let $$(X, \mathcal{B}, \mu, T)$$ be a dynamical system where X is compact metric space with Borel $$\sigma$$ -algebra $$\mathcal{B}$$ , and $$\mu$$ probability measure that ergodic respect to the homeomorphism $$T \colon \to X$$ . We study following differentiation problem: Given $$f \in C(X)$$ $$F_k \mathcal{B}$$ $$\mu(F_k) > 0$$ when can we say $$\lim_{k \infty} \frac{\int_{F_k} ( \frac{1}{k} \sum_{i = 0}^{k - 1} T^i f ) \, \mathrm{d} \mu}{\mu(F_k)} \int \mu \ ?$$ establish some sufficient conditions for these sequences converge.
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2022
ISSN: ['0001-5954', '0236-5294', '1588-2632']
DOI: https://doi.org/10.1007/s10474-022-01276-5