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MSC2020 · 28Axx

Classical measure theory

Classical measure theory

5 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

28A05Classes of sets (Borel fields,

\sigma

-rings, etc.), measurable sets, Suslin sets, analytic sets0 28A10Real- or complex-valued set functions0 28A12Contents, measures, outer measures, capacities0 28A15Abstract differentiation theory, differentiation of set functions0 28A20Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence0 28A25Integration with respect to measures and other set functions0 28A33Spaces of measures, convergence of measures0 28A35Measures and integrals in product spaces0 28A50Integration and disintegration of measures0 28A51Lifting theory0 28A60Measures on Boolean rings, measure algebras0 28A75Length, area, volume, other geometric measure theory5 28A78Hausdorff and packing measures0 28A80Fractals2 28A99Classical measure theory0

Mapped problems

OP-12115AnalysisStatus unassessed

3D Kakeya problem (AlphaEvolve problem 10)

3D Kakeya problem (AlphaEvolve problem 10). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12114AnalysisStatus unassessed

Kakeya needle problem (AlphaEvolve problem 9)

Kakeya needle problem (AlphaEvolve problem 9). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12074AnalysisOpen

Favard-length decay exponent ( $C_{60}$ )

Favard-length decay exponent: determine C 60 or improve its bounds; the repository records frac 1 6 (lower) and 1 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12044AnalysisOpen

Falconer distance problem in $\mathbb{R}^2$ ( $C_{34}$ )

Falconer distance problem in mathbb R ^2 : determine C 34 or improve its bounds; the repository records 1 (lower) and frac 5 4 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11995CombinatoricsOpen

Kakeya sums-differences constant ( $C_{3b}$ )

Kakeya sums-differences constant: determine C 3b or improve its bounds; the repository records 1.77898 (1.77898884 ) (lower) and 1.83333 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

Journals & articles in MSC 28

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Analysis & PDE ↗

Mathematical Sciences Publishers

Analysis and partial differential equations

Journal discovery is available; article-level extraction for this class is not yet included in this batch.

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MSC2020 © Mathematical Reviews (AMS) and zbMATH · CC BY-NC-SA 4.0 · Official PDF, page 67