Hausdorff Measure - Relation With Hausdorff Dimension

Relation With Hausdorff Dimension

One of several possible equivalent definitions of the Hausdorff dimension is

\operatorname{dim}_{\mathrm{Haus}}(S)=\inf\{d\ge 0:H^d(S)=0\}=\sup\bigl(\{d\ge 0:H^d(S)=\infty\}\cup\{0\}\bigr),

where we take

Read more about this topic:  Hausdorff Measure

Famous quotes containing the words relation with, relation and/or dimension:

    “To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.”
    —Henry James (1843–1916)

    “Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
    —Honoré De Balzac (1799–1850)

    “Authority is the spiritual dimension of power because it depends upon faith in a system of meaning that decrees the necessity of the hierarchical order and so provides for the unity of imperative control.”
    —Shoshana Zuboff (b. 1951)