Sentence examples for m is continuous from inspiring English sources

If p is in (1,∞)⧹{2}, and supt>0 ⦀M tL)⦀L p<∞, i.e., if M is an L puniform spectral multiplier of L in our terminology, and M is continuous on R+, then M extends to a bounded holomorphic function on the sector Sφp∗.

Since M is continuous, taking limit as n → ∞, we have M ( g ( a ), F ( a, b ), ϕ ( t ) ) = 1, which implies that F ( a, b ) = g ( a ) = x.

Consequently, M is continuous.

Then M is continuous function on X 2 × ( 0, ∞ ).

It is clear that m is continuous on J and (|m| = 1/200).

Also assume that g j , 1 ≤ j ≤ m is continuous on X.

Given that k is continuous, M is a strictly convex smooth Orlicz function and (MinDelta_{2}capnabla _{2}).

Firstly, we show that (A_{n, m}:Kto K) is continuous.

T and g are M-continuous and ( O, M ) -compatible; T and g are continuous and commuting; ( X, d, M ) is regular and gX is closed.

For each i = 1, 2, …, λ, noting that | g i ( m, y k ( m ) ) − g i ( m, y ( m ) ) | ≤ 2 μ i M ( m ), m ∈ Z, g i ( m, ⋅ ) is continuous for each m ∈ Z, and y k ( m ) → y ( m ) for each m ∈ Z, we conclude that ∥ g i ( ⋅, y k − g i ( ⋅, y ∥ p → 0. Combining this with (3.2), we know that N y k → N y.

Assume that the function F : ( X m, d ) → ( X m, d ) is continuous on X m and satisfies any one of the following conditions: (a) F is ( ≼ I, ≼ I ) -increasing;   (b) p is an even integer and F is ( ≼ I, ≼ I ) -decreasing.  .