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PureMathematics
n
Ø
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Æ
,2023,13(6),1744-1752
PublishedOnlineJune2023inHans.https://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2023.136178
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Radon
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AnIsomorphicVersionoftheLower
DimensionalBusemann-Petty
ProblemsforMeasures
XianyangZhu
Scho olofDateScience,TongrenUniversity,TongrenGuizhou
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[J].
n
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,2023,13(6):1744-1752.
DOI:10.12677/pm.2023.136178
Á
k
Received:May21
st
,2023;accepted:Jun.22
nd
,2023;published:Jun.30
th
,2023
Abstract
ThelowerdimensionalBusemann-Petty(LDBP)problemforarbitrarymeasuresasks:
ForagivenBorelmeasure
µ
withappropriatedensityandtwoorigin-symmetricconvex
bo dies
K
and
L
,doestheassumptionthat
µ
(
K
∩
ξ
⊥
)
≤
µ
(
L
∩
ξ
⊥
)
holdsforany
ξ
∈
G
(
n,i
)(1
≤
i<n
)
implythat
µ
(
K
)
≤
µ
(
L
)
?Itwasprovedthattheproblemhasthesame
answerasRubinandZhang’ssolutionstotheLDBPproblemforvolumes.Inthis
paperweshowanisomorphicversionofthisresult.Namely,iftheaboveconditions
hold,then
µ
(
K
)
≤
n
i/
2
µ
(
L
)
forany
1
≤
i
≤
n
.
Keywords
IsomorphicVersion,IntersectionBody,Measures,RadonTransform
Copyright
c
2023byauthor(s)andHansPublishersInc.
ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/pm.2023.1361781747
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