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:

    “[Man’s] life consists in a relation with all things: stone, earth, trees, flowers, water, insects, fishes, birds, creatures, sun, rainbow, children, women, other men. But his greatest and final relation is with the sun.”
    —D.H. (David Herbert)

    “Much poetry seems to be aware of its situation in time and of its relation to the metronome, the clock, and the calendar. ... The season or month is there to be felt; the day is there to be seized. Poems beginning “When” are much more numerous than those beginning “Where” of “If.” As the meter is running, the recurrent message tapped out by the passing of measured time is mortality.”
    —William Harmon (b. 1938)

    “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)