The decreasing rearrangements of functions for vector-valued measures

Chilin , V.I., Zakirova , G.B.

O‘zbekiston matematika jurnali · 2025-yil

Annotatsiya

Let $B$ be a complete Boolean algebra, let $Q(B)$ be the Stone compact of $B$, let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x:Q(B) \rightarrow [-\infty,+\infty],$ assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. We consider Maharam measure $m$ defined on $B$, which takes on value in the algebra $L^0(\Omega)$ of all real measurable functions on the measurable space $(\Omega, \Sigma, \mu)$ with a $\sigma$-finite numerical measure $\mu$. The decreasing rearrangements of functions from $C_\infty (Q(B))$, associated with such a measure $m$ and taking values in the algebra $L^0(\Omega)$ are determined. The basic properties of such rearrangements are established, which are similar to the properties of classical decreasing rearrangements of measurable functions.As an application, with the help of the property of equimeasurablity of elements from $ C_\infty (Q(B))$, associated with such a measure $m$, the notion of a symmetric Banach-Kantorovich space $(E,\|\cdot\|_{E})$ over $L^0(\Omega)$ is introduced and studied in detail. Here $E\subset C_\infty (Q(B)),$ and \ $\|\cdot\|_{E}$ -- $L^0(\Omega)$-valued norm in $E$, endowing it with the structure of the Banach-Kantorovich space. Examples of symmetric Banach-Kantorovich spaces are given, which are vector-valued analogues of classical $L^p$-spaces, $ 1\leq p \leq \infty$, associated with a numerical $\sigma$-finite measure.

Maqola ma’lumotlari
MualliflarChilin , V.I., Zakirova , G.B.
JurnalO‘zbekiston matematika jurnali
NashriyotЎзбекистон Республикаси ФА Математика институти
ISSN2010-7269
Nashr sanasi2025-11-03
Jild69
Son4
Betlar70-82
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.29229/uzmj.2025-4-8
Indeksga qo‘shilgan2026-08-26

DOI: 10.29229/uzmj.2025-4-8 · Maqolaning asl sahifasi

Kalit so‘zlar

vector integration, vector-valued measure, decreasing rearrangements, equimeasurablity, the Banach-Kantorovich lattice, symmetric space

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAChilin , V.I., & Zakirova , G.B. (2025). The decreasing rearrangements of functions for vector-valued measures. O‘zbekiston matematika jurnali, 69(4), 70-82. https://doi.org/10.29229/uzmj.2025-4-8
GOST (OAK)Chilin , V.I., Zakirova , G.B. The decreasing rearrangements of functions for vector-valued measures // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 70-82. – DOI: 10.29229/uzmj.2025-4-8.
MLAChilin , V.I., and Zakirova , G.B. “The decreasing rearrangements of functions for vector-valued measures.” O‘zbekiston matematika jurnali, 69(4), 70-82, 2025. https://doi.org/10.29229/uzmj.2025-4-8
ChicagoChilin , V.I., and Zakirova , G.B. “The decreasing rearrangements of functions for vector-valued measures.” O‘zbekiston matematika jurnali, 69(4), 70-82 (2025). https://doi.org/10.29229/uzmj.2025-4-8
HarvardChilin , V.I., and Zakirova , G.B (2025) ‘The decreasing rearrangements of functions for vector-valued measures’, O‘zbekiston matematika jurnali, 69(4), 70-82. https://doi.org/10.29229/uzmj.2025-4-8
BibTeX
@article{chilinvi2025,
  title = {The decreasing rearrangements of functions for vector-valued measures},
  author = {Chilin , V.I. and Zakirova , G.B.},
  journal = {O‘zbekiston matematika jurnali},
  year = {2025},
  volume = {69},
  number = {4},
  pages = {70-82},
  doi = {10.29229/uzmj.2025-4-8},
  url = {https://doi.org/10.29229/uzmj.2025-4-8}
}

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