The author obtains some extensions of Egoroff's condition to non-additive, Riesz space valued measures. Here \(\mathcal{F}\) is a \(\sigma\)-algebra of subsets of \(X\), \(V\) is a Riesz space and \(\mu: \mathcal{F} \to V\) is a non-additive measure, which means it is monotone with \( \mu(\emptyset) =0\). Some notations and definitions: (i) \(\mu\) is called continuous from above if \( A_{n} \downarrow A \) implies \(\mu( A_{n}) \downarrow \mu( A)\), and continuous from below if \( A_{n} \uparrow A \) implies \(\mu( A_{n}) \uparrow \mu( A)\). (ii) \(\mu\) is said to be strongly order continuous if \( A_{n} \downarrow A \) with \(\mu(A)=0\) implies \(\mu( A_{n}) \downarrow 0\). (iii) \(\mu\) is said to have the property \(\mathcal{S}\) if every sequence \(\{ A_{n} \}\), with \( \mu( A_{n}) \to 0\), has a subsequence \(\{ A_{n_{k}} \}\) such that \( \mu (\bigcap_{k=1}^{\infty} \bigcup_{i=k}^{\infty} A_{n_{i}})=0\). (iv) For a non-additive measure \(\mu\), a double sequence \( \{ A_{m,n} \}_{(m,n) \in \mathbb{N}^{2}} \subset \mathcal{F}\) is called a \(\mu\)-regulator in \(\mathcal{F}\) if it is decreasing in \(n\), \(\forall m\) and \(\mu(\bigcup_{m=1}^{\infty} \bigcap_{n=1}^{\infty} A_{m,n})=0\); \(\mu\) is said to satisfy Egoroff's condition if \(\inf_{\theta \in \Theta} \mu(\bigcup_{m=1}^{\infty} A_{m, \theta(m)})=0, \) for every \(\mu\)-regulator \( A_{m,n} \subset \mathcal{F}\) (here \(\Theta = \mathbb{N}^{\mathbb{N}})\). (v) A double sequence \( \{ r_{i,j} \} \subset V\) is called a regulator in \(V\) if it is order bounded, \( r_{i,j} \downarrow 0, \forall i\). \(V\) is said to have Egoroff's property if for regulator \( \{ r_{i,j} \} \subset V\), there exists a sequence \( \{ p_{k} \} \subset V\), \(p_{k} \downarrow 0\), such that for each \((k,i) \in \mathbb{N}^{2}\) there exists a \(j(k,i) \in \mathbb{N}\) such that \( r_{i,j(k,i)} \leq p_{k}\). (vi) \(\mu\) is said to be uniformly autocontinuous from above if for any sequence \( \{ B_{n} \} \subset \mathcal{F}\) with \( \mu ( B_{n} ) \to 0\), there is a sequence \(\{ p_{n} \} \subset V\), \(p_{n} \downarrow 0\), such that \( \mu ( B_{n} \cup A) \leq p_{n} + \mu ( A), \forall A \in \mathcal{F}, \forall n \). The main results of the paper are: I. Suppose (a) \(V \) is Dedekind \(\sigma\)-complete and has Egoroff's property, (b) \(\mu\) is strongly order continuous and has \(\mathcal{S}\) property. Then \(\mu\) satisfies Egoroff's condition. II. Suppose \(V \) is Dedekind \(\sigma\)-complete and weakly \(\sigma\)-distributive. If \(\mu\) is uniformly autocontinuous from above, strongly order continuous, and continuous from below, then \(\mu\) satisfies Egoroff's condition. III. Suppose \(\mu\) has Egoroff property. Then \(\mu\) has the property \(\mathcal{S}\) if and only if from any sequence \( \{ f_{n} \}\) of real-valued \(\mathcal{F}\)-measurable functions, converging in \(\mu\)-measure to an \(\mathcal{F}\)-measurable \(f\), one could extract a subsequence converging to \(f\) almost everywhere. Some additional related results and corollaries are also proved.