Dimension of images and graphs of little Lipschitz functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475610" target="_blank" >RIV/00216208:11320/23:10475610 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.8ejxeoocr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.8ejxeoocr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/fm147-12-2022" target="_blank" >10.4064/fm147-12-2022</a>

Result language
angličtina
Original language name
Dimension of images and graphs of little Lipschitz functions
Original language description
A mapping f : X -> Y between metric spaces is termed little Lipschitz if the function lip f : X -> [0, infinity], lip f (x) = lim inf(r -> 0) diam f(B(x, r))/r, is finite at every point. We prove that for each s > 0 the little Lipschitz mapping f satisfies the inequality H-s (f(X)) <= integral(X) (lip f)(s) dP(s) as long as {lip f = 0} is of sigma-finite measure P-s, where H-s and P-s denote the s-dimensional Hausdorff and packing measures, respectively. We derive a dimensional in-equality for little Lipschitz mappings dim(H) f (X) <= dim(H) f <= (dim) over bar (P) X and we provide a few examples that show that these inequalities are the best possible.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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