Critical point exponents inequalities - The Coopersmith inequolity

[LagrangeEuler]

The Coopersmith inequolity:
$$T=T_c, H\rightarrow 0^+$$

I'm confused by few things. What means $$H\rightarrow 0^+$$? And what difference will be if $$H\rightarrow 0^-$$? And what means $$T=T_c$$ if we can't measure $$T_c$$ in experiments?

Then there is relation $$M \sim H^{\frac{1}{\delta}}$$
That means if I understand well that
$$\frac{1}{\delta}=\lim_{H\rightarrow 0}\frac{lnM(H)}{lnH}$$
Correct?

 

[LagrangeEuler]

Any answer?