After following a discussion that Shamir's Secret Sharing scheme cannot be used to share a real number as secret, I came across the paper "Secret Sharing Over Infinite Domains" - B. Chor and E. Kushilevitz The above paper describes a method for sharing a real number as a secret, I quote from Section 4 (note: this paper may be accessed freely)
We first introduce a (k,k) secret-sharing scheme which distributes a secret a taken from the interval [0,1). We use the Lebesgue measure on [0,1) Choose independently, with a uniform distribution, k-1 real numbers, {$s_1$,.., $s_{k-1}$} in the interval [0,1). 2) Choose $s_k$ $\in$ [0,1) which satisfies $s_1$ +...+ $s_{k-1}$ +$s_{k}$ = a (mod 1). The proof that this is indeed a secret-sharing scheme is similar to the proof of its analogue in the finite case.
For introducing a (k ,n) secret-sharing scheme for every k $\leq$ n, we observe that the same technique described in [BL] works here as well.
I can see how this (k,k) threshold scheme works. However, I am having some issues with the (k,n) threshold scheme - I've tried to look at Generalized Secret Sharing and Monotone Functions which is referred to above as BL (note - this paper can also be accessed freely.) I don't see how this paper helps me construct a (k,n) threshold scheme.
Any help would be appreciated!