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It has been shown that Friedmann equation of FRW universe can be derived fromthe idea which says cosmic space is emergent as cosmic time progresses and ouruniverse is expanding towards the state with the holographic equipartition byPadmanabhan. In this note, we give a general relationship between the horizonentropy and the number of the degrees of freedom on the surface, we also obtainthe corresponding dynamic equations by using the idea of emergence of space inthe $f(R)$ theory and deformed Ho\v{r}ava-Lifshitz (HL) theory.

Emergence of spaces and the dynamic equations of FRW universes in the $f(R)$ theory and deformed Ho\v{r}ava-Lifshitz theory