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Martin Sleziak
Martin Sleziak
9:05 AM
-1
Q: Proof of equivalent definitions of $\dim_B F$ (box-dimension) of a subset $F \subset \mathbb R^n$ (Falconer)

epsilon-emperorMain Theme of Question: I aim to establish the equivalence of definitions of $\dim_B F$ (i.e. the box-counting dimension) for $F\subset\mathbb R^n$. Following is an extract from Kenneth Falconer's Fractal Geometry. The author proves (1) $\Leftrightarrow$ (4) and (1) $\Leftrightarrow$ (5). I need ...

real-analysis analysis solution-verification proof-explanation fractals
in CURED, 2 mins ago, by Martin Sleziak
@epsilon-emperor Looking at the tags at that question, the tag analysis seems mostly useless. Since it is about box dimension, maybe dimension-theory-analysis would be suitable?
There are some discussions on meta related to the analysis tag, such as: Should the (analysis) tag be deprecated? and How should the “analysis” tag be used?
 
Martin Sleziak
Martin Sleziak
9:55 AM
in CURED, 45 mins ago, by epsilon-emperor
Okay cool, let me edit the tags then
0
Q: Proof of equivalent definitions of $\dim_B F$ (box-dimension) of a subset $F \subset \mathbb R^n$ (Falconer)

epsilon-emperorMain Theme of Question: I aim to establish the equivalence of definitions of $\dim_B F$ (i.e. the box-counting dimension) for $F\subset\mathbb R^n$. Following is an extract from Kenneth Falconer's Fractal Geometry. The author proves (1) $\Leftrightarrow$ (4) and (1) $\Leftrightarrow$ (5). I need ...

real-analysis solution-verification proof-explanation fractals dimension-theory-analysis
 
 
7 hours later…
Arctic Char
Arctic Char
5:08 PM
Should we add the tag weak-convergence a question about "strong operator convergence"? The tag strong-convergence exists, but it refers to the usual convergence (in norm).
Related question, in particular there is some discussion in the comment section of the answer.
 

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