Seeking a constructive proof of a theorem of Khrushchev

Bartosz Malman

doi:10.1515/conop-2025-0011

January 1, 2026Concrete OperatorsOpen Access

Seeking a constructive proof of a theorem of Khrushchev

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Key Points

The aim is to provide a constructive proof of a classical theorem by Khrushchev regarding positive Lebesgue measure sets.
Discussion of the classical theorem
Analysis of continuous Cauchy transforms
Exploration of functions supported by positive measures
Validates that positive Lebesgue measure sets on the circle can support continuous functions
Confirms the existence of functions with continuous Cauchy transforms for these sets

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Abstract

We discuss a classical theorem of Khrushchev, which establishes that any set of positive Lebesgue measure on the circle supports a function with a continuous Cauchy transform.

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Bartosz Malman (2026) studied this question.

synapsesocial.com/papers/69994c9f873532290d021384 https://doi.org/10.1515/conop-2025-0011

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Seeking a constructive proof of a theorem of Khrushchev

Key Points

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Abstract

Discussion

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Seeking a constructive proof of a theorem of Khrushchev

Key Points

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Abstract

Discussion

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