Picard theorem and translation-invariant ergodic measures

Zhi‐Tao Wen; Xiao Yao; Zhuan Ye

doi:10.33205/cma.1879437

February 2, 2026Open Access

Picard theorem and translation-invariant ergodic measures

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Key Points

This research aims to establish a version of the Picard theorem within the context of function spaces described by translation-invariant probability measures.
Analyzed the properties of entire and meromorphic functions under translation-invariant measures.
Used mathematical proofs to derive results applicable in the ergodic measure theory.
Demonstrated the existence of translation-invariant ergodic measures within the function space.
Established the conditions under which this analogue of the Picard theorem holds, broadening the implications for function theory.

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Implication

Explores an analogue of Picard theorem with translation-invariant measures on function spaces, implying new insights in function theory.

Abstract

Weestablish an analogue of the classical Picard theorem in the setting of the space of entire or meromorphic functions with translation-invariant probability measures.

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Wen et al. (2026) studied this question.

synapsesocial.com/papers/6a362e91db0793dc1a536472 https://doi.org/10.33205/cma.1879437

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Picard theorem and translation-invariant ergodic measures

Key Points

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Implication

Abstract

Discussion

Cite This Study

Picard theorem and translation-invariant ergodic measures

Key Points

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Implication

Abstract

Discussion

Cite This Study

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